solve for X
m * e^2 * g * h + 2 * m * g * X + (m * g^2) / (2 * k) = (k / 2) * ( (m * g) / k + X )^2
You asked:
Solve the equation \[m \cdot {e}^{2} \cdot g h + 2 m g X + \frac{m \cdot {g}^{2}}{2 k} = \frac{k}{2} \cdot {\left( \frac{m g}{k} + X \right)}^{2}\] for the unknown \(X\).
MathBot Answer:
$$\begin{aligned}X &= \frac{g m}{k} + \frac{\sqrt{g m \left(g + 2 h k e^{2}\right)}}{k}\\X &= \frac{g m}{k} - \frac{\sqrt{g m \left(g + 2 h k e^{2}\right)}}{k}\end{aligned}$$