Answer
$-2-\frac{\sqrt{3}}{3}\ i$; $-2+\frac{\sqrt{3}}{3}\ i$
Work Step by Step
Given \begin{equation}
3 x^2+12 x+15=2.
\end{equation} This equation can be best solved by using the quadratic formula.
\begin{equation}
\begin{aligned}
3 x^2+12 x+15&=2\\
3 x^2+12 x+13&=0\\
x&=\frac{-12 \pm \sqrt{12^2-4 \cdot 3 \cdot 13}}{2 \cdot 3}\\
x&= \frac{-12 \pm \sqrt{-12} i}{6}\\
x&=\frac{-12 \pm 2 \sqrt{3} i}{6}\\
&= -2\pm \frac{\sqrt{3}}{3}\ i.
\end{aligned}
\end{equation} The solution is \begin{equation}
x= -2-\frac{\sqrt{3}}{3}\ i\ ,\quad x= -2+ \frac{\sqrt{3}}{3}\ i.
\end{equation}
