\(\displaystyle{3}{x}{\left({x}-{l}\right)}={2}+{6}\)

Apply the distributive property \(\displaystyle{3}{x}^{{{2}}}-{3}{x}={x}+{6}\)

Subtract «+ 6 from each side \(\displaystyle{3}{x}^{{{2}}}-{3}{x}—{x}-{6}={0}\)

\(\displaystyle{3}{x}^{{{2}}}-{4}{x}-{6}={0}\)

By the quadratic formula \(\displaystyle{x}={\frac{{-{\left(-{4}\right)}\pm\sqrt{{{\left(-{4}\right)}^{{2}}-{4}{\left({3}\right)}{\left(-{6}\right)}}}}}{{{2}{\left({3}\right)}}}}\)

\(\displaystyle{x}={\frac{{{4}\pm\sqrt{{88}}}}{{6}}}={\frac{{{4}\pm\sqrt{{4}}\cdot{22}}}{{6}}}{)}\)

\(\displaystyle{x}={\frac{{{4}}}{{{6}}}}\pm{\frac{{{2}\sqrt{{{22}}}}}{{6}}}\)

\(\displaystyle{x}={\frac{{{2}}}{{{3}}}}\pm{\frac{{\sqrt{{{22}}}}}{{{3}}}}\)

Apply the distributive property \(\displaystyle{3}{x}^{{{2}}}-{3}{x}={x}+{6}\)

Subtract «+ 6 from each side \(\displaystyle{3}{x}^{{{2}}}-{3}{x}—{x}-{6}={0}\)

\(\displaystyle{3}{x}^{{{2}}}-{4}{x}-{6}={0}\)

By the quadratic formula \(\displaystyle{x}={\frac{{-{\left(-{4}\right)}\pm\sqrt{{{\left(-{4}\right)}^{{2}}-{4}{\left({3}\right)}{\left(-{6}\right)}}}}}{{{2}{\left({3}\right)}}}}\)

\(\displaystyle{x}={\frac{{{4}\pm\sqrt{{88}}}}{{6}}}={\frac{{{4}\pm\sqrt{{4}}\cdot{22}}}{{6}}}{)}\)

\(\displaystyle{x}={\frac{{{4}}}{{{6}}}}\pm{\frac{{{2}\sqrt{{{22}}}}}{{6}}}\)

\(\displaystyle{x}={\frac{{{2}}}{{{3}}}}\pm{\frac{{\sqrt{{{22}}}}}{{{3}}}}\)