Answer
The solutions are $-5$ and $5$.
Work Step by Step
$ 2x^{2}-8=42\qquad$ ...divide entire expression with $2$.
$ x^{2}-4=21\qquad$ ...add $4$ to each side.
$x^{2}-4+4=21+4$
$ x^{2}=25\qquad$ ...take square roots of each side.
$ x=\pm\sqrt{25}\qquad$ ...evaluate $\sqrt{25}$
$x=\pm 5$
