Answer
$x_{1}= -\dfrac{3}{2} + \dfrac{\sqrt{15}i}{2}$ and $x_{2} = -\dfrac{3}{2} - \dfrac{\sqrt{15}i}{2}$
Work Step by Step
Given $x^2+3x+6=0$
$a= 1, \ b=3, \ c=6$
Using the quadratic formula: $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$ we have:
$\dfrac{-3 \pm \sqrt{3^2-4 \times 1\times 6}}{2 \times 1} = \dfrac{-3 \pm \sqrt{9-24}}{2} = \dfrac{-3 \pm \sqrt{-15}}{2} = \dfrac{-3 \pm \sqrt{15}i}{2} = -\dfrac{3}{2} \pm \dfrac{\sqrt{15}i}{2}$
Therefore the solutions are $x_{1}= -\dfrac{3}{2} + \dfrac{\sqrt{15}i}{2}$ and $x_{2} = -\dfrac{3}{2} - \dfrac{\sqrt{15}i}{2}$
