Add 24 to both sides of the equation: $\displaystyle{{x}}^{{2}}-{8}{x}+{24}={0}\usepackage{cmbright}\Huge\$

Substitute $\displaystyle{a}={1},{b}=-{8}\usepackage{cmbright}\Huge\$ , and $\displaystyle{c}={24}\usepackage{cmbright}\Huge\$ into the Quadratic Formula:

$\displaystyle{x}=\frac{{-{b}\pm\sqrt{{{{b}}^{{2}}-{4}{a}{c}}}}}{{{2}{a}}}\usepackage{cmbright}\Huge\$

$\displaystyle{x}=\frac{{-{\left(-{8}\right)}\pm\sqrt{{{{\left(-{8}\right)}}^{{2}}-{4}{\left({1}\right)}{\left({24}\right)}}}}}{{{2}\cdot{1}}}=\frac{{{8}\pm\sqrt{{{64}-{96}}}}}{{2}}=\frac{{{8}\pm\sqrt{{-{32}}}}}{{2}}\usepackage{cmbright}\Huge\$

$\displaystyle=\frac{{{8}\pm\sqrt{{16}}\sqrt{{-{2}}}}}{{2}}=\frac{{{8}\pm{4}\sqrt{{2}}{i}}}{{2}}=\frac{{8}}{{2}}\pm\frac{{{4}\sqrt{{2}}}}{{2}}{i}={4}\pm{2}{i}\sqrt{{2}}\usepackage{cmbright}\Huge\$