Answer
$\displaystyle -\frac{3}{2}\pm\frac{\sqrt{19}}{2}i$
Work Step by Step
$\displaystyle x^{2}+3x+7=0$
We use the quadratic formula ($a=1, b=3, c=7$):
$\displaystyle x=\frac{-3\pm\sqrt{3^{2}-4*1*7}}{2(1)}=\frac{-3\pm\sqrt{-19}}{2}=-\frac{3}{2}\pm\frac{\sqrt{19}}{2}i$