Math Problem Solver

$$\begin{aligned}t &= - \frac{S^{2}}{3 u^{2} \sqrt[3]{- \frac{S^{3}}{u^{3}} + \frac{\sqrt{- \frac{4 S^{6}}{u^{6}} + \left(- \frac{2 S^{3}}{u^{3}} + \frac{27}{2 a u}\right)^{2}}}{2} + \frac{27}{4 a u}}} + \frac{S}{3 u} - \frac{\sqrt[3]{- \frac{S^{3}}{u^{3}} + \frac{\sqrt{- \frac{4 S^{6}}{u^{6}} + \left(- \frac{2 S^{3}}{u^{3}} + \frac{27}{2 a u}\right)^{2}}}{2} + \frac{27}{4 a u}}}{3}\\t &= - \frac{S^{2}}{3 u^{2} \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{S^{3}}{u^{3}} + \frac{\sqrt{- \frac{4 S^{6}}{u^{6}} + \left(- \frac{2 S^{3}}{u^{3}} + \frac{27}{2 a u}\right)^{2}}}{2} + \frac{27}{4 a u}}} + \frac{S}{3 u} - \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{S^{3}}{u^{3}} + \frac{\sqrt{- \frac{4 S^{6}}{u^{6}} + \left(- \frac{2 S^{3}}{u^{3}} + \frac{27}{2 a u}\right)^{2}}}{2} + \frac{27}{4 a u}}}{3}\\t &= - \frac{S^{2}}{3 u^{2} \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{S^{3}}{u^{3}} + \frac{\sqrt{- \frac{4 S^{6}}{u^{6}} + \left(- \frac{2 S^{3}}{u^{3}} + \frac{27}{2 a u}\right)^{2}}}{2} + \frac{27}{4 a u}}} + \frac{S}{3 u} - \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{- \frac{S^{3}}{u^{3}} + \frac{\sqrt{- \frac{4 S^{6}}{u^{6}} + \left(- \frac{2 S^{3}}{u^{3}} + \frac{27}{2 a u}\right)^{2}}}{2} + \frac{27}{4 a u}}}{3}\end{aligned}$$ and \(t \neq 0\)