Answer
$x=-1\pm\dfrac{\sqrt{6}}{6}i$
Work Step by Step
$6x^{2}+12x+7=0$
Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=6$, $b=12$ and $c=7$.
Substitute the known values in the formula:
$x=\dfrac{-12\pm\sqrt{12^{2}-4(6)(7)}}{2(6)}=\dfrac{-12\pm\sqrt{144-168}}{122}=...$
$...=\dfrac{-12\pm\sqrt{-24}}{12}=\dfrac{-12\pm2\sqrt{6}i}{12}=-1\pm\dfrac{\sqrt{6}}{6}i$
The answer is $x=-1\pm\dfrac{\sqrt{6}}{6}i$
