Given quadratic equation is \(\displaystyle{2}{x}^{{2}}−{6}{x}+{5}={0}.\)

Standard equation of quadratic equation is \(\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}\).

On comparing the given equation with standard equation of quadratic equation, we get a=2, b=−6 and c=5

Quadratic formula is given as:

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

Therefore, solving given quadratic equation with quadratic formula,

\(\displaystyle{x}=\frac{{-{\left(-{6}\right)}\pm\sqrt{{{\left(-{6}\right)}^{{2}}-{4}{\left({2}\right)}{\left({5}\right)}}}}}{{2}}{\left({2}\right)}\)

\(\displaystyle=\frac{{{6}\pm\sqrt{{{36}-{40}}}}}{{4}}\)

\(\displaystyle=\frac{{{6}\pm\sqrt{-}{4}}}{{4}}\)

\(\displaystyle={\left({6}\pm\frac{\sqrt{{{4}{i}}}}{{4}}{\left(\sqrt{-}{1}={i}\right)}\right)}\)

\(\displaystyle=\frac{{{6}\pm{2}{i}}}{{4}}\)

\(\displaystyle=\frac{{{3}\pm{i}}}{{2}}\)

Therefore, required solution of given quadratic equation is: x=(3+i)/2 or x=(3-i)/2