Add x to both sides: $\displaystyle{{x}}^{{2}}+{x}+\frac{{7}}{{4}}={0}\usepackage{cmbright}\Huge\$

Substitute $\displaystyle{a}={1},{b}={1}\usepackage{cmbright}\Huge\$ , and $\displaystyle{c}=\frac{{7}}{{4}}\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{{-{1}\pm\sqrt{{{{1}}^{{2}}-{4}{\left({1}\right)}{\left(\frac{{7}}{{4}}\right)}}}}}{{{2}\cdot{1}}}=\frac{{-{1}\pm\sqrt{{{1}-{7}}}}}{{2}}=\frac{{-{1}\pm\sqrt{{-{6}}}}}{{2}}=\frac{{-{1}\pm{i}\sqrt{{6}}}}{{2}}\usepackage{cmbright}\Huge\$