# Manipulating output from Solve

I have two systems of equations Linear in $A_i$

System 1

$\sum_{i=1}^{4} A_i F_{a1i}(H_1,H_2,H_3,H_4) = G_{a1}(H_1,H_2,H_3,H_4) \\ \sum_{i=1}^{4} A_i F_{a2i}(H_1,H_2,H_3,H_4) = G_{a2}(H_1,H_2,H_3,H_4)\\ \sum_{i=1}^{4} A_i F_{a3i}(H_1,H_2,H_3,H_4) = G_{a3}(H_1,H_2,H_3,H_4) \\ \sum_{i=1}^{4} A_i F_{a4i}(H_1,H_2,H_3,H_4) = G_{a4}(H_1,H_2,H_3,H_4)\\$

System 2

$\sum_{i=1}^{4} A_i F_{b1i}(H_1,H_2,H_3,H_4) = G_{b1}(H_1,H_2,H_3,H_4) \\ \sum_{i=1}^{4} A_i F_{b2i}(H_1,H_2,H_3,H_4) = G_{b2}(H_1,H_2,H_3,H_4)\\ \sum_{i=1}^{4} A_i F_{b3i}(H_1,H_2,H_3,H_4) = G_{b3}(H_1,H_2,H_3,H_4) \\ \sum_{i=1}^{4} A_i F_{b4i}(H_1,H_2,H_3,H_4) = G_{b4}(H_1,H_2,H_3,H_4)\\$

I'm doing something like this:

sol1={A1,A2,A3,A4}/.Solve[{system1},{A1,A2,A3,A4}];
sol2={A1,A2,A3,A4}/.Solve[{system2},{A1,A2,A3,A4}];


I want to use solutions of $A_1,A_2,A_3,A_4$ from system 1 and equate it to solutions for $A_1,A_2,A_3,A_4$ from system 2 and solve for $H_1,H_2,H_3,H_4$.

Since the expressions for $A_i$ are huge and non-linear in $H_i$, I am hoping to Manipulate and ContourPlot these equations to get a handle on what the starting points should be for my FindRoot.

But Manipulate requires explicitly stating the dependent variables, so something like this won't work:

Manipulate[ContourPlot[sol1[[1,1]]-sol2[[1,1]],{H1,a,b},{H2,c,d}],{H3,e,f},{H4,g,h}]


Short of copy and pasting these unwieldy expressions, how do I get the expressions for A1 and A2 from my Solve to inside a Manipulate?

Here is an actual expression for A1, where H0S,H0D,HSS and HDD are the His. OK, I couldn't enter the entire expressions since I exceeded the 30000 characters limit to I will just chop the expression so it fits.

sol1[[1,1]]=

-(1. H0S^4.00018 (0. + 2.32831*10^-10 H0D^19.2389 H0S^0.85 -
2.72848*10^-12 H0D^20.2389 H0S^0.85 +
443050. H0D^17.1804 H0S^2.90842 +
575155. H0D^17.1804 H0S^3.05842 -
7817.16 H0D^17.1804 H0S^3.90842 +
3.32944*10^7 H0D^14.2088 H0S^5.88008 -
1.17688*10^7 H0D^14.3588 H0S^5.88008 -
422897. H0D^15.2088 H0S^5.88008 -
3.18462*10^7 H0D^13.8554 H0S^6.23351 +
1.11936*10^7 H0D^14.0054 H0S^6.23351 +
383811. H0D^14.8554 H0S^6.23351 +
9.74273*10^6 H0D^12.1504 H0S^7.93851 +
1.11936*10^7 H0D^12.1504 H0S^8.08851 -
1.01858*10^7 H0D^11.7969 H0S^8.29194 -
1.17688*10^7 H0D^11.7969 H0S^8.44194 -
76762.2 H0D^12.1504 H0S^8.93851 +
84579.3 H0D^11.7969 H0S^9.29194 -
1.4482*10^6 H0D^8.82527 H0S^11.2636 +
575155. H0D^8.97527 H0S^11.2636 +
39085.8 H0D^9.82527 H0S^11.2636 +
5.82077*10^-11 H0D^9.47184 H0S^11.617))/(H0D^6.76685 \
(-7.27596*10^-12 H0D^10.767 H0S^4.85018 +
5420.07 H0D^10.4136 H0S^5.20361 -
1.09787*10^6 H0D^5.73694 H0S^9.88027 +
2.1849*10^6 H0D^5.38351 H0S^10.2337 -
1.09787*10^6 H0D^5.03008 H0S^10.5871 +
5420.07 H0D^0.353429 H0S^15.2638 -
2.18279*10^-11 H0S^15.6172)) + (1. (-0.0499415 H0D^18.3889 \
H0S^4.85018 + 5.93956*10^14 H0D^16.3304 H0S^6.9086 +
3.8147*10^-6 H0D^16.3304 H0S^8.96703 -
1.36551*10^16 H0D^13.3588 H0S^9.88027 +
1.30612*10^16 H0D^13.0054 H0S^10.2337 +
8.53953*10^-13 H0D^18.3889 H0S^10.2337 +
1.30612*10^16 H0D^11.3004 H0S^11.9387 -
10156.1 H0D^16.3304 H0S^12.2921 -
1.36551*10^16 H0D^10.9469 H0S^12.2921 +
5.93956*10^14 H0D^7.97527 H0S^15.2638 +
233490. H0D^13.3588 H0S^15.2638 -
223334. H0D^13.0054 H0S^15.6172 +
3.8147*10^-6 H0D^7.97527 H0S^17.3222 -
223334. H0D^11.3004 H0S^17.3222 +
233490. H0D^10.9469 H0S^17.6756 -
10156.1 H0D^7.97527 H0S^20.6473) (0. + (136170. +
1702.13 (-8.08817 - 1. H0D)) (-7.60629*10^9 -
5106.38 H0S^3.32509)))/(H0D^5.91685 H0S^2.05842 \
(-7.60629*10^9 -
5106.38 H0S^3.32509) (-7.27596*10^-12 H0D^10.767 H0S^4.85018 +
5420.07 H0D^10.4136 H0S^5.20361 -
1.09787*10^6 H0D^5.73694 H0S^9.88027 +
2.1849*10^6 H0D^5.38351 H0S^10.2337 -
1.09787*10^6 H0D^5.03008 H0S^10.5871 +
5420.07 H0D^0.353429 H0S^15.2638 -
2.18279*10^-11 H0S^15.6172) (-1. (-7.60629*10^9 -
5106.38 H0D^3.32509) (-0.13006 - 5106.38/
H0S^2.05842) + (-0.13006 - 5106.38/
H0D^2.05842) (-7.60629*10^9 -
5106.38 H0S^3.32509))) + (1. ((32768. H0D^16.3304 H0S^6.9086 \
+ 0.0166472 H0D^18.3889 H0S^7.82184 +
0.00980853 H0D^18.3889 H0S^8.17527 -
1.97985*10^14 H0D^16.3304 H0S^9.88027 -
1.16653*10^14 H0D^16.3304 H0S^10.2337 +
4.55171*10^15 H0D^13.3588 H0S^12.8519 -
4.35373*10^15 H0D^13.0054 H0S^13.2054 +
2.68187*10^15 H0D^13.3588 H0S^13.2054 -
2.56522*10^15 H0D^13.0054 H0S^13.5588 -
4.35373*10^15 H0D^11.3004 H0S^14.9104 +
32768. H0D^7.97527 H0S^15.2638 +
4.55171*10^15 H0D^10.9469 H0S^15.2638 -
2.56522*10^15 H0D^11.3004 H0S^15.2638 +
2.68187*10^15 H0D^10.9469 H0S^15.6172 -
1.97985*10^14 H0D^7.97527 H0S^18.2354 -
1.16653*10^14 H0D^7.97527 H0S^18.5889)/(H0D^5.91685 \
(-7.60629*10^9 -
5106.38 H0S^3.32509) (-7.27596*10^-12 H0D^10.767 \
H0S^4.85018 + 5420.07 H0D^10.4136 H0S^5.20361 -
1.09787*10^6 H0D^5.73694 H0S^9.88027 +
2.1849*10^6 H0D^5.38351 H0S^10.2337 -
1.09787*10^6 H0D^5.03008 H0S^10.5871 +
5420.07 H0D^0.353429 H0S^15.2638 -
2.18279*10^-11 H0S^15.6172)) - (1. (-0.0499415 H0D^18.3889 \
H0S^4.85018 + 5.93956*10^14 H0D^16.3304 H0S^6.9086 +
3.8147*10^-6 H0D^16.3304 H0S^8.96703 -
1.36551*10^16 H0D^13.3588 H0S^9.88027 +
1.30612*10^16 H0D^13.0054 H0S^10.2337 +
8.53953*10^-13 H0D^18.3889 H0S^10.2337 +
1.30612*10^16 H0D^11.3004 H0S^11.9387 -
10156.1 H0D^16.3304 H0S^12.2921 -
1.36551*10^16 H0D^10.9469 H0S^12.2921 +
5.93956*10^14 H0D^7.97527 H0S^15.2638 +
233490. H0D^13.3588 H0S^15.2638 -
223334. H0D^13.0054 H0S^15.6172 +
3.8147*10^-6 H0D^7.97527 H0S^17.3222 -
223334. H0D^11.3004 H0S^17.3222 +
233490. H0D^10.9469 H0S^17.6756 -
10156.1 H0D^7.97527 H0S^20.6473) (-1. (-7.60629*10^9 -
5106.38 H0D^3.32509) (-1.49388*10^9 +
1702.13 H0S^2.97166) + (-1.49388*10^9 +
1702.13 H0D^2.97166) (-7.60629*10^9 -
5106.38 H0S^3.32509)))/(H0D^5.91685 H0S^2.05842 \
(-7.60629*10^9 -
5106.38 H0S^3.32509) (-7.27596*10^-12 H0D^10.767 \
H0S^4.85018 + 5420.07 H0D^10.4136 H0S^5.20361 -
1.09787*10^6 H0D^5.73694 H0S^9.88027 +
2.1849*10^6 H0D^5.38351 H0S^10.2337 -
1.09787*10^6 H0D^5.03008 H0S^10.5871 +
5420.07 H0D^0.353429 H0S^15.2638 -
2.18279*10^-11 H0S^15.6172) (-1. (-7.60629*10^9 -
5106.38 H0D^3.32509) (-0.13006 - 5106.38/
H0S^2.05842) + (-0.13006 - 5106.38/
H0D^2.05842) (-7.60629*10^9 -
5106.38 H0S^3.32509)))) ((-1. (-7.60629*10^9 -
5106.38 H0D^3.32509) (-0.13006 - 5106.38/
H0S^2.05842) + (-0.13006 - 5106.38/
H0D^2.05842) (-7.60629*10^9 -
5106.38 H0S^3.32509)) (0. + (-7.60629*10^9 -
5106.38 H0S^3.32509) (80. (-22929.8 H0D^2.33151 -

1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)) +
1702.13 (4.86301 H0D^0.266667 (-3.06484 H0D^2.06484 \
(-72.2455 - 0.909091 HDD) + 0.0909091 HDD^3.06484) -
1. (-3.06484 (-0.777709 - 0.0909091 H0D) H0D^2.06484 -
0.0909091 H0D^3.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)))) -
1. (0. + (136170. +
1702.13 (-8.08817 - 1. H0D)) (-7.60629*10^9 -
5106.38 H0S^3.32509)) ((-7.60629*10^9 -
5106.38 H0S^3.32509) (1702.13 (4.86301 H0D^0.266667 (0. + \
(2.05842 HDD^3.06484)/H0D^3.05842) +
5.12326 H0D^0.00641587 (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)) -
0.0000764104 (-22929.8 H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817))) -
1. (-0.13006 - 5106.38/
H0S^2.05842) (-4.46869*10^6 (-22929.8 H0D^2.33151 -
1. (0. -

501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)) +
1702.13 (-0.260251 H0D^5.38993 (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817) +
4.86301 H0D^0.266667 (0. -
3.32509 H0D^2.32509 HDD^3.06484))))))/(-1. (-1. \
(-7.60629*10^9 - 5106.38 H0D^3.32509) (-1.49388*10^9 +
1702.13 H0S^2.97166) + (-1.49388*10^9 +
1702.13 H0D^2.97166) (-7.60629*10^9 -
5106.38 H0S^3.32509)) ((-7.60629*10^9 -
5106.38 H0S^3.32509) (1702.13 (4.86301 H0D^0.266667 (0. + (
2.05842 HDD^3.06484)/H0D^3.05842) +
5.12326 H0D^0.00641587 (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/H0D^2.79817)) -
0.0000764104 (-22929.8 H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817))) -
1. (-0.13006 - 5106.38/
H0S^2.05842) (-4.46869*10^6 (-22929.8 H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/H0D^2.79817)) +
1702.13 (-0.260251 H0D^5.38993 (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/H0D^2.79817) +
4.86301 H0D^0.266667 (0. -
3.32509 H0D^2.32509 HDD^3.06484)))) + (-1. \
(-7.60629*10^9 - 5106.38 H0D^3.32509) (-0.13006 - 5106.38/
H0S^2.05842) + (-0.13006 - 5106.38/
H0D^2.05842) (-7.60629*10^9 -
5106.38 H0S^3.32509)) ((-7.60629*10^9 -
5106.38 H0S^3.32509) (-877653. (-22929.8 H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/H0D^2.79817)) +
1702.13 (0.0931782 H0D^5.0365 (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/H0D^2.79817) +
4.86301 H0D^0.266667 (0. -
2.97166 H0D^1.97166 HDD^3.06484))) -
1. (-1.49388*10^9 +
1702.13 H0S^2.97166) (-4.46869*10^6 (-22929.8 H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/H0D^2.79817)) +

1702.13 (-0.260251 H0D^5.38993 (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/H0D^2.79817) +
4.86301 H0D^0.266667 (0. -
3.32509 H0D^2.32509 HDD^3.06484))))) + (1. \
((0.0166472 H0D^18.3889 H0S^4.85018 -
1.97985*10^14 H0D^16.3304 H0S^6.9086 +
4.55171*10^15 H0D^13.3588 H0S^9.88027 +
4.34803*10^-12 H0D^18.3889 H0S^9.88027 -
4.35373*10^15 H0D^13.0054 H0S^10.2337 -
51711.2 H0D^16.3304 H0S^11.9387 +
0.000244141 H0D^13.0054 H0S^11.9387 -
4.35373*10^15 H0D^11.3004 H0S^11.9387 +
4.55171*10^15 H0D^10.9469 H0S^12.2921 +
0.000244141 H0D^11.3004 H0S^13.6437 +
1.18885*10^6 H0D^13.3588 H0S^14.9104 -
1.97985*10^14 H0D^7.97527 H0S^15.2638 -
1.13714*10^6 H0D^13.0054 H0S^15.2638 -
1.13714*10^6 H0D^11.3004 H0S^16.9688 +
1.18885*10^6 H0D^10.9469 H0S^17.3222 -
51711.2 H0D^7.97527 H0S^20.2939)/(H0D^5.91685 H0S^1.70499 \
(-7.60629*10^9 -
5106.38 H0S^3.32509) (-7.27596*10^-12 H0D^10.767 \
H0S^4.85018 + 5420.07 H0D^10.4136 H0S^5.20361 -
1.09787*10^6 H0D^5.73694 H0S^9.88027 +
2.1849*10^6 H0D^5.38351 H0S^10.2337 -
1.09787*10^6 H0D^5.03008 H0S^10.5871 +
5420.07 H0D^0.353429 H0S^15.2638 -
2.18279*10^-11 H0S^15.6172)) - (1. (-0.0499415 H0D^18.3889 \
H0S^4.85018 + 5.93956*10^14 H0D^16.3304 H0S^6.9086 +
3.8147*10^-6 H0D^16.3304 H0S^8.96703 -
1.36551*10^16 H0D^13.3588 H0S^9.88027 +
1.30612*10^16 H0D^13.0054 H0S^10.2337 +
8.53953*10^-13 H0D^18.3889 H0S^10.2337 +
1.30612*10^16 H0D^11.3004 H0S^11.9387 -
10156.1 H0D^16.3304 H0S^12.2921 -
1.36551*10^16 H0D^10.9469 H0S^12.2921 +
5.93956*10^14 H0D^7.97527 H0S^15.2638 +
233490. H0D^13.3588 H0S^15.2638 -
223334. H0D^13.0054 H0S^15.6172 +
3.8147*10^-6 H0D^7.97527 H0S^17.3222 -
223334. H0D^11.3004 H0S^17.3222 +
233490. H0D^10.9469 H0S^17.6756 -
10156.1 H0D^7.97527 H0S^20.6473) (-1. (-7.60629*10^9 -
5106.38 H0D^3.32509) (-0.662221 + 1702.13/
H0S^1.70499) + (-0.662221 + 1702.13/
H0D^1.70499) (-7.60629*10^9 -
5106.38 H0S^3.32509)))/(H0D^5.91685 H0S^2.05842 \
(-7.60629*10^9 -
5106.38 H0S^3.32509) (-7.27596*10^-12 H0D^10.767 \
H0S^4.85018 + 5420.07 H0D^10.4136 H0S^5.20361 -
1.09787*10^6 H0D^5.73694 H0S^9.88027 +
2.1849*10^6 H0D^5.38351 H0S^10.2337 -
1.09787*10^6 H0D^5.03008 H0S^10.5871 +
5420.07 H0D^0.353429 H0S^15.2638 -
2.18279*10^-11 H0S^15.6172) (-1. (-7.60629*10^9 -
5106.38 H0D^3.32509) (-0.13006 - 5106.38/
H0S^2.05842) + (-0.13006 - 5106.38/
H0D^2.05842) (-7.60629*10^9 -
5106.38 H0S^3.32509))) - (1. ((32768. H0D^16.3304 \
H0S^6.9086 + 0.0166472 H0D^18.3889 H0S^7.82184 +
0.00980853 H0D^18.3889 H0S^8.17527 -
1.97985*10^14 H0D^16.3304 H0S^9.88027 -
1.16653*10^14 H0D^16.3304 H0S^10.2337 +
4.55171*10^15 H0D^13.3588 H0S^12.8519 -
4.35373*10^15 H0D^13.0054 H0S^13.2054 +
2.68187*10^15 H0D^13.3588 H0S^13.2054 -
2.56522*10^15 H0D^13.0054 H0S^13.5588 -
4.35373*10^15 H0D^11.3004 H0S^14.9104 +
32768. H0D^7.97527 H0S^15.2638 +
4.55171*10^15 H0D^10.9469 H0S^15.2638 -
2.56522*10^15 H0D^11.3004 H0S^15.2638 +
2.68187*10^15 H0D^10.9469 H0S^15.6172 -
1.97985*10^14 H0D^7.97527 H0S^18.2354 -
1.16653*10^14 H0D^7.97527 H0S^18.5889)/(H0D^5.91685 \
(-7.60629*10^9 -
5106.38 H0S^3.32509) (-7.27596*10^-12 H0D^10.767 \
H0S^4.85018 + 5420.07 H0D^10.4136 H0S^5.20361 -
1.09787*10^6 H0D^5.73694 H0S^9.88027 +
2.1849*10^6 H0D^5.38351 H0S^10.2337 -
1.09787*10^6 H0D^5.03008 H0S^10.5871 +
5420.07 H0D^0.353429 H0S^15.2638 -
2.18279*10^-11 H0S^15.6172)) - (1. (-0.0499415 \
H0D^18.3889 H0S^4.85018 + 5.93956*10^14 H0D^16.3304 H0S^6.9086 +
3.8147*10^-6 H0D^16.3304 H0S^8.96703 -
1.36551*10^16 H0D^13.3588 H0S^9.88027 +
1.30612*10^16 H0D^13.0054 H0S^10.2337 +
8.53953*10^-13 H0D^18.3889 H0S^10.2337 +
1.30612*10^16 H0D^11.3004 H0S^11.9387 -
10156.1 H0D^16.3304 H0S^12.2921 -
1.36551*10^16 H0D^10.9469 H0S^12.2921 +
5.93956*10^14 H0D^7.97527 H0S^15.2638 +
233490. H0D^13.3588 H0S^15.2638 -
223334. H0D^13.0054 H0S^15.6172 +
3.8147*10^-6 H0D^7.97527 H0S^17.3222 -
223334. H0D^11.3004 H0S^17.3222 +
233490. H0D^10.9469 H0S^17.6756 -
10156.1 H0D^7.97527 H0S^20.6473) (-1. (-7.60629*10^9 \
- 5106.38 H0D^3.32509) (-1.49388*10^9 +
1702.13 H0S^2.97166) + (-1.49388*10^9 +
1702.13 H0D^2.97166) (-7.60629*10^9 -
5106.38 H0S^3.32509)))/(H0D^5.91685 H0S^2.05842 \
(-7.60629*10^9 -
5106.38 H0S^3.32509) (-7.27596*10^-12 H0D^10.767 \
H0S^4.85018 + 5420.07 H0D^10.4136 H0S^5.20361 -
1.09787*10^6 H0D^5.73694 H0S^9.88027 +
2.1849*10^6 H0D^5.38351 H0S^10.2337 -
1.09787*10^6 H0D^5.03008 H0S^10.5871 +
5420.07 H0D^0.353429 H0S^15.2638 -
2.18279*10^-11 H0S^15.6172) (-1. (-7.60629*10^9 -
5106.38 H0D^3.32509) (-0.13006 - 5106.38/
H0S^2.05842) + (-0.13006 - 5106.38/
H0D^2.05842) (-7.60629*10^9 -
5106.38 H0S^3.32509)))) (-1. (-1. (-7.60629*10^9 -
5106.38 H0D^3.32509) (-0.662221 + 1702.13/
H0S^1.70499) + (-0.662221 + 1702.13/
H0D^1.70499) (-7.60629*10^9 -
5106.38 H0S^3.32509)) ((-7.60629*10^9 -
5106.38 H0S^3.32509) (1702.13 (4.86301 H0D^0.266667 \
(0. + (2.05842 HDD^3.06484)/H0D^3.05842) +
5.12326 H0D^0.00641587 (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)) -
0.0000764104 (-22929.8 H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817))) -
1. (-0.13006 - 5106.38/
H0S^2.05842) (-4.46869*10^6 (-22929.8 H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)) +
1702.13 (-0.260251 H0D^5.38993 (-((
3.06484 H0D^2.06484)/HDD^1.79817) - (
1.79817 HDD^3.06484)/H0D^2.79817) +
4.86301 H0D^0.266667 (0. -
3.32509 H0D^2.32509 HDD^3.06484)))) + (-1. \
(-7.60629*10^9 - 5106.38 H0D^3.32509) (-0.13006 - 5106.38/
H0S^2.05842) + (-0.13006 - 5106.38/
H0D^2.05842) (-7.60629*10^9 -
5106.38 H0S^3.32509)) ((-7.60629*10^9 -
5106.38 H0S^3.32509) (-0.000389055 (-22929.8 \
H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)) +
1702.13 (-1. (-1.70499 H0D^0.359845 -
3.06484 H0D^0.359845) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817) +
4.86301 H0D^0.266667 (0. + (1.70499 HDD^3.06484)/
H0D^2.70499))) -
1. (-0.662221 + 1702.13/
H0S^1.70499) (-4.46869*10^6 (-22929.8 H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)) +
1702.13 (-0.260251 H0D^5.38993 (-((
3.06484 H0D^2.06484)/HDD^1.79817) - (
1.79817 HDD^3.06484)/H0D^2.79817) +
4.86301 H0D^0.266667 (0. -
3.32509 H0D^2.32509 HDD^3.06484))))))/(-1. (-1. \
(-7.60629*10^9 - 5106.38 H0D^3.32509) (-1.49388*10^9 +
1702.13 H0S^2.97166) + (-1.49388*10^9 +
1702.13 H0D^2.97166) (-7.60629*10^9 -
5106.38 H0S^3.32509)) ((-7.60629*10^9 -
5106.38 H0S^3.32509) (1702.13 (4.86301 H0D^0.266667 \
(0. + (2.05842 HDD^3.06484)/H0D^3.05842) +
5.12326 H0D^0.00641587 (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)) -
0.0000764104 (-22929.8 H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817))) -
1. (-0.13006 - 5106.38/
H0S^2.05842) (-4.46869*10^6 (-22929.8 H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)) +
1702.13 (-0.260251 H0D^5.38993 (-((
3.06484 H0D^2.06484)/HDD^1.79817) - (
1.79817 HDD^3.06484)/H0D^2.79817) +
4.86301 H0D^0.266667 (0. -
3.32509 H0D^2.32509 HDD^3.06484)))) + (-1. \
(-7.60629*10^9 - 5106.38 H0D^3.32509) (-0.13006 - 5106.38/
H0S^2.05842) + (-0.13006 - 5106.38/
H0D^2.05842) (-7.60629*10^9 -
5106.38 H0S^3.32509)) ((-7.60629*10^9 -
5106.38 H0S^3.32509) (-877653. (-22929.8 H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)) +
1702.13 (0.0931782 H0D^5.0365 (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817) +
4.86301 H0D^0.266667 (0. -
2.97166 H0D^1.97166 HDD^3.06484))) -
1. (-1.49388*10^9 +
1702.13 H0S^2.97166) (-4.46869*10^6 (-22929.8 \
H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)) +
1702.13 (-0.260251 H0D^5.38993 (-((
3.06484 H0D^2.06484)/HDD^1.79817) - (
1.79817 HDD^3.06484)/H0D^2.79817) +
4.86301 H0D^0.266667 (0. -
3.32509 H0D^2.32509 HDD^3.06484)))))) ((-1. (-1. \
(-7.60629*10^9 - 5106.38 H0D^3.32509) (-1.49388*10^9 +
1702.13 H0S^2.97166) + (-1.49388*10^9 +
1702.13 H0D^2.97166) (-7.60629*10^9 -
5106.38 H0S^3.32509)) ((-7.60629*10^9 -
5106.38 H0S^3.32509) (1702.13 (4.86301 H0D^0.266667 \
(0. + (2.05842 HDD^3.06484)/H0D^3.05842) +
5.12326 H0D^0.00641587 (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)) -
0.0000764104 (-22929.8 H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817))) -
1. (-0.13006 - 5106.38/
H0S^2.05842) (-4.46869*10^6 (-22929.8 H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)) +
1702.13 (-0.260251 H0D^5.38993 (-((
3.06484 H0D^2.06484)/HDD^1.79817) - (
1.79817 HDD^3.06484)/H0D^2.79817) +
4.86301 H0D^0.266667 (0. -
3.32509 H0D^2.32509 HDD^3.06484)))) + (-1. \
(-7.60629*10^9 - 5106.38 H0D^3.32509) (-0.13006 - 5106.38/
H0S^2.05842) + (-0.13006 - 5106.38/
H0D^2.05842) (-7.60629*10^9 -
5106.38 H0S^3.32509)) ((-7.60629*10^9 -

5106.38 H0S^3.32509) (-877653. (-22929.8 H0D^2.33151 -
1. (0. -
501.61 H0D^2.06484) (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817)) +
1702.13 (0.0931782 H0D^5.0365 (-((3.06484 H0D^2.06484)/
HDD^1.79817) - (1.79817 HDD^3.06484)/
H0D^2.79817) +
4.86301 H0D^0.266667 (0. -
2.97166 H0D^1.97166 HDD^3.06484))) -
1. (-1.49388*10^9 +
1702.13 H0S^2.

-
Manipulate requires explicitly stating the dependent variables, then, why not explicitly stating the dependent? I guess something like f[H1_, H2_]=sol1[[1, 1]]; g[H3_, H4_]=sol2[[1, 1]]; Manipulate[ContourPlot[f[H1, H2] - g[H3, H4], {H1, a, b}, {H2, c, d}], {H3, e, f}, {H4, g, h}]  will work. –  xzczd Apr 8 '13 at 3:24
@xzczd Thank you! I didn't realize I could do that. –  Amatya Apr 8 '13 at 20:38
@xzcd I just realized that for the past 3 days I was doing f[H1_,H2_] := sol1[[1,1]]; and it was "working" for my FindRoot but today when I tried to Plot it it didn't work and then I noticed you wrote "=" instead of ":=". Can you please explain why we'e not using ":=" here.. or I can post a separate question for this if you like. –  Amatya Apr 11 '13 at 20:39
Well, to be honest, I can't explain this clearly, the only thing I know is that f[H1_,H2_] := Evaluate@sol1[[1,1]] will also work. In fact, I used to ask a similiar question(See the first two sample I gave there) but maybe that question is a little messy, so I don't get a very good answer for this part. I suggest you to post a new question if you want to get a better understanding for this. –  xzczd Apr 12 '13 at 5:57