Answer
The solutions are $x=\left\{-2, 2\right\}$.
Work Step by Step
Use the property $a^m = a^n \longrightarrow m=n$ to obtain:
$\begin{array}{ccc}
&2x^2-3&=&9-x^2
\\&2x^2-3+x^2&=&9-x^2+x^2
\\&3x^2-3&=&9
\\&3x^2-3+3&=&9+3
\\&3x^2&=&12
\\&\dfrac{3x^2}{3} &= &\dfrac{12}{3}
\\&x^2&=&4
\\&\sqrt{x^2}&=&\pm\sqrt{4}
\\&x&=&\pm2
\end{array}$
Thus, the solutions are $x=\left\{-2, 2\right\}$.
