Answer
$\color{blue}{\left\{-4-\sqrt{46}, -4+\sqrt{46}\right\}}$
Work Step by Step
The solutions of the quadratic equation $ax^2+bx+c=0$ can be found using the quadratic formula:
$$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$
Write the given equation in $ax^2+bx+c=0$ form to obtain:
$$x^2+8x-30=0$$
The equation above has $a=1, b=8, \text{ and } c= -30$.
Substitute these values into the quadratic formula to obtain:
\begin{align*}
x&=\frac{-8\pm\sqrt{8^2-4(1)(-30)}}{2(1)}\\\\
x&=\frac{-8\pm \sqrt{64+120}}{2}\\\\
x&=\frac{-8\pm \sqrt{184}}{2}\\\\
x&=\frac{-8\pm\sqrt{4(46)}}{2}\\\\
x&=\frac{-8\pm1\sqrt{46}}{2}
\end{align*}
Thus,
$x_1=\dfrac{-8+2\sqrt{46}}{2}=-4+\sqrt{46}\\\\$
$x_2=\dfrac{-8-2\sqrt{46}}{2}=4+\sqrt{46}$
Therefore, the solution set is $\color{blue}{\left\{-4-\sqrt{46}, -4+\sqrt{46}\right\}}$.
