Question

$2^{2x^{2 }+3x-2$ =8

Answer 1

$2^{2x^2+3x-2}=2^3 \implies 2x^2+3x-2=3\implies2x^2+3x-5=0$
$\Delta=3^2-4\times2\times(-5)=9+40=49$
$x_1=\frac{-3+\sqrt{49}}{2\times2}=\frac{-3+7}{4}=1$
$x_2=\frac{-3-7}{4}=\frac{-10}{4}=-\frac{5}{2}$