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Mathematica is taking forever to solve the following equation. Is there any other way t solve this equation for x?

Solve[Sum[(i*((1 - (Sum[
         Binomial[7, j]*x^(7 - j)*(1 - x)^j, {j, 0, 6}])^
       i)^240 - (1 - (Sum[
         Binomial[7, j]*x^(7 - j)*(1 - x)^j, {j, 0, 6}])^(i - 
         1))^240)), {i, 1, 10}] == 5, x]
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sum = Sum[(i*((1 - (Sum[
             Binomial[7, j]*x^(7 - j)*(1 - x)^j, {j, 0, 6}])^
           i)^240 - (1 - (Sum[
             Binomial[7, j]*x^(7 - j)*(1 - x)^j, {j, 0, 6}])^(i - 
             1))^240)), {i, 1, 10}];

FindRoot[sum == 5, {x, 0}]

{x -> 0.0421849}

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  • $\begingroup$ Could you please tell me how to plot the corresponding graph of x as a function of n (I had kept n as a constant value 6 in above equation)? $\endgroup$ – Scissor Jun 1 '16 at 14:05
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Since n is an integer a list plot is appropriate.

sols = Table[{n, FindRoot[sum[n] == 5, {x, 0.1}]}, {n, 1, 6}]

Convert to points

pnts = sols /. ({x -> y_} -> y)

Plot

ListPlot[pnts, Filling -> Axis, PlotRange -> {All, {0, 1}}]
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