#### Answer

$\frac{3}{4}\pm\frac{\sqrt{7}}{4}i$

#### Work Step by Step

$2x^{2}-3x+2=0$
We use the quadratic formula ($a=2, b=-3, c=2$):
$x=\frac{-\ -3\pm\sqrt{(-3)^{2}-4*2*2}}{2*2}=\frac{3\pm\sqrt{9-16}}{4}=\frac{3\pm\sqrt{-7}}{4}=\frac{3}{4}\pm\frac{\sqrt{7}}{4}i$