Answer
$ t=\sqrt{\frac{s-s_{0}-k}{g}},\qquad t=-\sqrt{\frac{s-s_{0}-k}{g}};,\qquad\quad g\neq 0$
Work Step by Step
Switch sides
$s_{0}+g^{2}+k=s$
Subtract $s_{0}+k$ from both sides and simplify
$s_{0}+g^{2}+k-\left(z_{0}+k\right)=z-\left(s_{0}+k\right)$
$gt^{2}=s-\left(s_{0}+k\right)$
Divide both sides by $g;\quad g\neq 0$
$ t^{2}=\displaystyle \frac{s-s_{0}-k}{g};,\qquad g\neq 0$
For $x^{2}=f(a)$ the solutions are $x=\sqrt{f(a)},-\sqrt{f(a)}$
$ t=\sqrt{\frac{s-s_{0}-k}{g}},\qquad t=-\sqrt{\frac{s-s_{0}-k}{g}};,\qquad\quad g\neq 0$
