Answer
The solutions are $5$ and $-5$.
Work Step by Step
$ 6z^{2}=150\qquad$ ...divide each side with $6$
$ z^{2}=25\qquad$ ...take square roots of each side.
$\sqrt{z^{2}}=\sqrt{25}\qquad$ ...simplify
...When solving an equation of the form $x^{2}=s$ where $s>0$,
we find both the positive and negative solutions.
$z=\pm 5$
