Simplify this quadratic equation

\(\displaystyle{8}{x}^{{2}}−{24}{x}+{18}={0}\)

\(\displaystyle{4}{x}^{{2}}−{12}{x}+{9}={0}\)

We know that,

The standard quadratic equation is: \(\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}\)

Quadratic formula is: \(\displaystyle{x}=\frac{{−{b}\pm\sqrt{{{b}^{{2}}−{4}{a}{c}}}}}{{{2}{a}}}\)

Here, a=4, b=−12, c=9

Let's apply the quadratic formula

\(\displaystyle{x}={\left(-{\left(-{12}\right)}\pm\frac{\sqrt{{{\left(-{12}\right)}^{{2}}-{4}{\left({4}\right)}{\left({9}\right)}}}}{{{2}{\left({4}\right)}}}\right.}\)

\(\displaystyle{x}=\frac{{{12}\pm\sqrt{{{144}-{144}}}}}{{8}}\)

\(\displaystyle{x}=\frac{{12}}{{8}}\)

\(\displaystyle{x}=\frac{{3}}{{2}}\)

\(\displaystyle{8}{x}^{{2}}−{24}{x}+{18}={0}\)

\(\displaystyle{4}{x}^{{2}}−{12}{x}+{9}={0}\)

We know that,

The standard quadratic equation is: \(\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}\)

Quadratic formula is: \(\displaystyle{x}=\frac{{−{b}\pm\sqrt{{{b}^{{2}}−{4}{a}{c}}}}}{{{2}{a}}}\)

Here, a=4, b=−12, c=9

Let's apply the quadratic formula

\(\displaystyle{x}={\left(-{\left(-{12}\right)}\pm\frac{\sqrt{{{\left(-{12}\right)}^{{2}}-{4}{\left({4}\right)}{\left({9}\right)}}}}{{{2}{\left({4}\right)}}}\right.}\)

\(\displaystyle{x}=\frac{{{12}\pm\sqrt{{{144}-{144}}}}}{{8}}\)

\(\displaystyle{x}=\frac{{12}}{{8}}\)

\(\displaystyle{x}=\frac{{3}}{{2}}\)