The Left hand side of the equation has only real part. But the right hand side has real and imaginary parts. So i am using a contour plot. The intersection of lefthand side and righthand side of plot gives my solution. But can anyone tell me how to find the intersection points? I tried using Findroot. But that gives me an error message "The line search decreased the step size to within tolerance specified by AccuracyGoal and PrecisionGoal but was unable to find a sufficient \ decrease in the merit function. You may need more than MachinePrecision digits of working precision to meet these tolerances. Can anyone help me with this problem? The code is as follows
d1[x_, r_] := 2^(1/3)/m^(1/3)*AiryAi[-2^((1/3))/m^(1/3)*((a*x*r) - m)];
e1[x_, r_] :=
2^(2/3)/m*AiryAiPrime[-(2^((1/3))/m^((1/3)))*((a*x*r) - m)];
f1[x_, r_] := d1[x, r] + e1[x, r];
g1[x_, r_] := 2^(1/3)/m^(1/3)*AiryAi[-2^((1/3))/m^(1/3)*((b*x*r) - m)];
h1[x_, r_] :=
2^(2/3)/m*AiryAiPrime[-(2^((1/3))/m^((1/3)))*((b*x*r) - m)];
i1[x_, r_] := g1[x, r] + h1[x, r];
j1[x_, r_] := -2^((1/3))/m^(1/3)*
AiryBi[-2^((1/3))/m^(1/3)*((b*x*r) - m)];
k1[x_, r_] := -2^((2/3))/m*
AiryBiPrime[-(2^((1/3))/m^((1/3)))*((b*x*r) - m)];
l1[x_, r_] := j1[x, r] + k1[x, r];
l2[x_, r_] := I*l1[x, r];
p1[x_, r_] := i1[x, r] + l2[x, r];
p2[x_] := p1[x, r] /. r -> 175*10^(-6);
f2[x_] := f1[x, r] /. r -> 175*10^(-6);
q1[x_, r_] := D[f1[x, r], r];
q2[x_] := q1[x, r] /. r -> 175*10^(-6);
q3[x_, r_] := D[p1[x, r], r];
q5[x_] := q3[x, r] /. r -> 175*10^(-6);
FindRoot[q2[x]/f2[x] == q5[x]/p2[x], {x, 8.9*10^(14)},
AccuracyGoal -> Infinity]
ContourPlot[
q2[x]/f2[x] == q5[x]/p2[x], {x, 1*10^(14), 2*10^(15)}, {y, 1*10^(14),
2*10^(15)}]