Answer
$\color{blue}{\left\{-4, 1\right\}}$
Work Step by Step
Recall
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 $a=3, b=9, \text{ and } c= -125$.
Substitute these values into the quadratic formula to obtain:
\begin{align*}
x&=\frac{-9\pm\sqrt{9^2-4(3)(-12)}}{2(3)}\\\\
x&=\frac{-9\pm \sqrt{81+144}}{6}\\\\
x&=\frac{-9\pm \sqrt{225}}{6}\\\\
x&=\frac{-9\pm 15}{6}\\\\
\end{align*}
Thus,
$x_1=\dfrac{-9+15}{6}=\dfrac{6}{6}=1\\\\$
$x_2=\dfrac{-9-15}{6}=\dfrac{-24}{6}=-4$
Therefore, the solution set is $\color{blue}{\left\{-4, 1\right\}}$.