Answer
$x=\pm 2$
Work Step by Step
We solve by factoring:
$2x^{4}-5x^{2}-12=0$
$(2x^{2}+3)(x^{2}-4)=0$
$2x^{2}+3=0$ or $x^{2}-4=0$
$2x^{2}=-3$ or $x^{2}=4$
$x^2=\frac{-3}{2}$ or $x^2=4$
$x=\pm\sqrt{\frac{-3}{2}}$=not real or $x=\pm\sqrt{4}$
$x=\pm 2$
We ignore the unreal solution.