Answer
$\color{blue}{\left\{-5, -3\right\}}$
Work Step by Step
The solutions of the quadratic equation $ax^2+bx+c=0$ can be found using the quadratic formula:
$$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$
The given quadratic equation has $a=1, b=8, \text{ and } c= 15$.
Substitute these values into the quadratic formula to obtain:
\begin{align*}
x&=\frac{-8\pm\sqrt{8^2-4(1)(15)}}{2(1)}\\\\
x&=\frac{-8\pm \sqrt{64-60}}{2}\\\\
x&=\frac{-8\pm \sqrt{4}}{2}\\\\
x&=\frac{-8\pm 2}{2}\\\\
\end{align*}
Thus,
$x_1=\dfrac{-8-2}{2}=\dfrac{-10}{2}=-5\\\\$
$x_2=\dfrac{-8+2}{2}=\dfrac{-6}{2}=-3$
Therefore, the solution set is $\color{blue}{\left\{-5, -3\right\}}$.
