Answer
$\{-4\pm \sqrt { 11}\}$.
Work Step by Step
The standard form the quadratic equation is
$\Rightarrow ax^2+bx+c=0$
The solutions for the standard form can be calculated with the Quadratic formula
$\Rightarrow x=\frac{-b\pm \sqrt {b^2-4ac}}{2a}$
Compare the given equation with the standard form and identify $a$, $b$, $c$:
$a=1,b=8$ and $c=5$
The solutions are
$\Rightarrow x=\frac{-8\pm \sqrt {8^2-4(1)(5)}}{2(1)}$
Simplify.
$\Rightarrow x=\frac{-8\pm \sqrt {64-20}}{2}$
$\Rightarrow x=\frac{-8\pm \sqrt {44}}{2}$
$\Rightarrow x=\frac{-8\pm \sqrt {2^2\cdot 11}}{2}$
$\Rightarrow x=\frac{-8\pm 2 \sqrt { 11}}{2}$
Factor out $2$.
$\Rightarrow x=\frac{2(-4\pm \sqrt { 11})}{2}$
Cancel common term $2$.
$\Rightarrow x=-4\pm \sqrt { 11}$.
The solution set is $\{-4\pm \sqrt { 11}\}$.
