# Solve the quadratic equation using the quadratic formula. 2x^2 - 6x + 5 = 0

Question
Solve the quadratic equation using the quadratic formula. $$\displaystyle{2}{x}^{{2}}-{6}{x}+{5}={0}$$

2021-02-22
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

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