[Physics] Calculating time using SUVAT equations with unknown initial velocity

Question

I understand that the equation used to find the equation used to find displacement when the initial velocity is unknown is:

$vt-(at^2)/2$

how would you rearrange this to solve for $t\;?$ When I try I get $t$ on both sides of the equation.

Answer 1

You can rearrange using the quadratic formula to get: $$ t = \frac{-u±\sqrt(u^2+2as)}{a} $$ Thanks AccidentalFourierTransform for the answer.