Answer
$x=\dfrac{-3\pm i\sqrt{15}}{2}$
Work Step by Step
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solutions of the given quadratic equation, $
x^2+3x+6=0
,$ are
\begin{array}{l}\require{cancel}
x=\dfrac{-3\pm\sqrt{3^2-4(1)(6)}}{2(1)}
\\\\
x=\dfrac{-3\pm\sqrt{9-24}}{2}
\\\\
x=\dfrac{-3\pm\sqrt{-15}}{2}
\\\\
x=\dfrac{-3\pm\sqrt{-1}\cdot\sqrt{15}}{2}
\\\\
x=\dfrac{-3\pm i\sqrt{15}}{2}
.\end{array}