#### Answer

$x_{1}= \dfrac{-1 + 3\sqrt{3}i}{2}$ and $x_{2}= \dfrac{-1\ - 3\sqrt{3}i}{2}$

#### Work Step by Step

Given $x^2+x+7=0$
$a=1,\ b=1,\ c=7$
Using the quadratic formula: $\dfrac{-b\pm \sqrt{b^2-4ac}}{2a} , $ we have:
$\dfrac{-1\pm \sqrt{1^2-4\times 1\times 7}}{2\times 1} = \dfrac{-1\pm \sqrt{-27}}{2} = \dfrac{-1\pm \sqrt{27}i}{2} = \dfrac{-1\pm 3\sqrt{3}i}{2}$
Therefore the solutions are: $x_{1}= \dfrac{-1 + 3\sqrt{3}i}{2}$ and $x_{2}= \dfrac{-1\ - 3\sqrt{3}i}{2}$