Answer
$\displaystyle -1\pm\frac{\sqrt{6}}{6}i$
Work Step by Step
$6x^{2}+12x+7=0$
We use the quadratic formula ($a=6, b=12, c=7$):
$x=\displaystyle \frac{-12\pm\sqrt{(12)^{2}-4*6*7}}{2(6)}=\frac{-12\pm\sqrt{144-168}}{12}=\frac{-12\pm\sqrt{-24}}{12}=\frac{-12\pm 2\sqrt{6}i}{12}=\frac{-12}{12}\pm\frac{2\sqrt{6}i}{12}=-1\pm\frac{\sqrt{6}}{6}i$
