Answer
$\left\{-3-\sqrt{5},-3+\sqrt{5}\right\}$
Work Step by Step
Using $ax^2+bx+c=0,$ the given equation, $
n^2+6n+4=0
,$ has
\begin{align*}
a=
1
,\text{ }b=
6
,\text{ and }c=
4
.\end{align*}
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, then
\begin{align*}\require{cancel}
x&=
\dfrac{-6\pm\sqrt{6^2-4(1)(4)}}{2(1)}
\\\\&=
\dfrac{-6\pm\sqrt{36-16}}{2}
\\\\&=
\dfrac{-6\pm\sqrt{20}}{2}
\\\\&=
\dfrac{-6\pm\sqrt{4\cdot5}}{2}
\\\\&=
\dfrac{-6\pm2\sqrt{5}}{2}
\\\\&=
\dfrac{-\cancelto36\pm\cancelto12\sqrt{5}}{\cancelto12}
\\\\&=
-3\pm\sqrt{5}
.\end{align*}
Hence, the solution set of the equation $
n^2+6n+4=0
$ is $\left\{-3-\sqrt{5},-3+\sqrt{5}\right\}$.
