The quadratic formula used for quadratic equation \(\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}\) is,

\(\displaystyle{x}=-\frac{{{b}\pm\sqrt{{{b}^{{2}}-{4}{a}{c}}}}}{{{2}{a}}}\)

Here, \(a=1, b=5 ,c=2\)

Substitute the given values in the quadratic formula as,

\(\displaystyle{x}=\frac{{-{5}\pm\sqrt{{{25}-{20}}}}}{{2}}\)

\(\displaystyle{x}=\frac{{-{5}\pm\sqrt{{5}}}}{{2}}\)

Hence, the solution for the equation is \(\displaystyle{x}=\frac{{-{5}+\sqrt{{5}}}}{{2}}{\quad\text{and}\quad}{x}=\frac{{-{5}-\sqrt{{5}}}}{{2}}\)