Answer
$\color{blue}{\left\{-3, -2\right\}}$.
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 $a=1, b=5, \text{ and } c= 6$.
Substitute these values into the quadratic formula to obtain:
\begin{align*}
x&=\frac{-5\pm\sqrt{5^2-4(1)(6)}}{2(1)}\\\\
x&=\frac{-5\pm \sqrt{25-24}}{2}\\\\
x&=\frac{-5\pm \sqrt{1}}{2}\\\\
x&=\frac{-5\pm 1}{2}\\\\
\end{align*}
Thus,
$x_1=\dfrac{-5-1}{2}=\dfrac{-6}{2}=-3\\\\$
$x_2=\dfrac{-5+1}{2}=\dfrac{-4}{2}=-2$
Therefore, the solution set is $\color{blue}{\left\{-3, -2\right\}}$.
