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## Homework Statement

After I differentiate a mathematical model, I got the following equation.

I wonder whether or not it is possible to solve c with the following equation

[tex] 0=c^3\,\left(\ifrac{3\,\left(A^2+c\,A\right)^{\frac{4}{3}}}{c^{\frac{8}{3}}}-\ifrac{24\,\left(A^2+c\,A\right)^{\frac{2}{3}}}{c^{\frac{4}{3}}}+20\right)+c\,\left(-\ifrac{12\,A^2\,\left(A^2+c\,A\right)^{\frac{2}{3}}}{c^{\frac{4}{3}}}-\ifrac{4\,A^2\,\left(A^2+c\,A\right)^{\frac{1}{3}}}{c^{\frac{2}{3}}}\right)+c^5\,\left(\ifrac{72\,\left(A^2+c\,A\right)^{\frac{2}{3}}}{c^{\frac{4}{3}}}-44\right)+c^2\,\left(9\,A-\ifrac{2\,A\,\left(A^2+c\,A\right)^{\frac{1}{3}}}{c^{\frac{2}{3}}}\right)+7\,A^3-40\,c^4\,A[/tex]

where A will be a possible integer

Can it be done analytically, or the numerical method is a possible solution.

## Homework Equations

## The Attempt at a Solution

Thanks