Answer
Solution set = $\{-5, -3\}.$
Work Step by Step
Quadratic formula: $\displaystyle \quad x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$x^{2}+8x+15=0 \quad \rightarrow \left\{\begin{array}{l}
a=1\\
b=8\\
c=15
\end{array}\right.$
$x=\displaystyle \frac{-8\pm\sqrt{8^{2}-4(1)(15)}}{2(1)}=\frac{-8\pm\sqrt{64-60}}{2}$
$=\displaystyle \frac{-8\pm\sqrt{4}}{2}=\frac{-8\pm 2}{2}$
$ x=\displaystyle \frac{-8-2}{2}=\frac{-10}{2}=-5\qquad$ or
$x=\displaystyle \frac{-8+2}{2}=\frac{-6}{2}=-3$
Solution set = $\{-5, -3\}.$
