Answer
$\displaystyle \frac{3}{2}\pm\frac{\sqrt{3}}{2}i$
Work Step by Step
$x^{2}-3x+3=0$
We use the quadratic formula ($a=1, b=-3, c=3$):
$\displaystyle x=\frac{-(-3)\pm\sqrt{(-3)^{2}-4*1*3}}{2(1)}=\frac{3\pm\sqrt{9-12}}{2}=\frac{3\pm\sqrt{-3}}{2}=\frac{3\pm \sqrt{3}i}{2}=\frac{3}{2}\pm\frac{\sqrt{3}}{2}i$
