Answer
$\color{blue}{\left\{-3, 15\right\}}$
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 $a=1, b=-12, \text{ and } c= -45$.
Substitute these values into the quadratic formula to obtain:
\begin{align*}
x&=\frac{-(-12)\pm\sqrt{(-12)^2-4(1)(-45)}}{2(1)}\\\\
x&=\frac{12\pm \sqrt{144+180}}{2}\\\\
x&=\frac{12\pm \sqrt{324}}{2}\\\\
x&=\frac{12\pm 18}{2}\\\\
\end{align*}
Thus,
$x_1=\dfrac{12+18}{2}=\dfrac{30}{2}=15\\\\$
$x_2=\dfrac{12-18}{2}=\dfrac{-6}{2}=-3$
Therefore, the solution set is $\color{blue}{\left\{-3, 15\right\}}$.
