Given:

\(\displaystyle{6}{x}^{{2}}+{5}{x}-{1}\)

The roots of \(\displaystyle{a}{x}^{{2}}+{b}{x}+{c}\) are

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

The roots of

\(\displaystyle{6}{x}^{{2}}+{5}{x}-{1}\)

\(\displaystyle{x}={\frac{{-{5}\pm\sqrt{{{5}^{{2}}-{4}{\left({6}\right)}{\left(-{1}\right)}}}}}{{{2}{\left({6}\right)}}}}\)

\(\displaystyle{x}={\frac{{-{5}\pm\sqrt{{{25}+{24}}}}}{{{12}}}}\)

\(\displaystyle{x}={\frac{{-{5}\pm\sqrt{{{49}}}}}{{{12}}}}\)

\(\displaystyle{x}={\frac{{-{5}\pm{7}}}{{{12}}}}\)

\(\displaystyle{x}=-{\frac{{{12}}}{{{12}}}},{\frac{{{2}}}{{{12}}}}\)

\(\displaystyle{x}=-{1},{\frac{{{1}}}{{{6}}}}\)

The roots of \(\displaystyle{6}{x}^{{2}}+{5}{x}-{1}\) are x=-1,\(\displaystyle{\frac{{{1}}}{{{6}}}}\)

The roots of

\(\displaystyle{4}{x}^{{2}}+{4}{x}-{4}\)

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

\(\displaystyle{x}={\frac{{-{4}\pm\sqrt{{{16}+{64}}}}}{{{8}}}}\)

\(\displaystyle{x}={\frac{{-{4}+\sqrt{{{80}}}}}{{{8}}}}\)

\(\displaystyle{x}={\frac{{-{4}\pm{4}\sqrt{{{5}}}}}{{{8}}}}\)

\(\displaystyle{x}=-{\frac{{{1}}}{{{2}}}}+{\frac{{\sqrt{{{5}}}}}{{{2}}}},-{\frac{{{1}}}{{{2}}}}-{\frac{{\sqrt{{{5}}}}}{{{2}}}}\)

The roots of \(\displaystyle{4}{x}^{{2}}+{4}{x}-{4}\) are \(\displaystyle{x}=-{\frac{{{1}}}{{{2}}}}+{\frac{{\sqrt{{{5}}}}}{{{2}}}},-{\frac{{{1}}}{{{2}}}}-{\frac{{\sqrt{{{5}}}}}{{{2}}}}\)

\(\displaystyle{6}{x}^{{2}}+{5}{x}-{1}\)

The roots of \(\displaystyle{a}{x}^{{2}}+{b}{x}+{c}\) are

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

The roots of

\(\displaystyle{6}{x}^{{2}}+{5}{x}-{1}\)

\(\displaystyle{x}={\frac{{-{5}\pm\sqrt{{{5}^{{2}}-{4}{\left({6}\right)}{\left(-{1}\right)}}}}}{{{2}{\left({6}\right)}}}}\)

\(\displaystyle{x}={\frac{{-{5}\pm\sqrt{{{25}+{24}}}}}{{{12}}}}\)

\(\displaystyle{x}={\frac{{-{5}\pm\sqrt{{{49}}}}}{{{12}}}}\)

\(\displaystyle{x}={\frac{{-{5}\pm{7}}}{{{12}}}}\)

\(\displaystyle{x}=-{\frac{{{12}}}{{{12}}}},{\frac{{{2}}}{{{12}}}}\)

\(\displaystyle{x}=-{1},{\frac{{{1}}}{{{6}}}}\)

The roots of \(\displaystyle{6}{x}^{{2}}+{5}{x}-{1}\) are x=-1,\(\displaystyle{\frac{{{1}}}{{{6}}}}\)

The roots of

\(\displaystyle{4}{x}^{{2}}+{4}{x}-{4}\)

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

\(\displaystyle{x}={\frac{{-{4}\pm\sqrt{{{16}+{64}}}}}{{{8}}}}\)

\(\displaystyle{x}={\frac{{-{4}+\sqrt{{{80}}}}}{{{8}}}}\)

\(\displaystyle{x}={\frac{{-{4}\pm{4}\sqrt{{{5}}}}}{{{8}}}}\)

\(\displaystyle{x}=-{\frac{{{1}}}{{{2}}}}+{\frac{{\sqrt{{{5}}}}}{{{2}}}},-{\frac{{{1}}}{{{2}}}}-{\frac{{\sqrt{{{5}}}}}{{{2}}}}\)

The roots of \(\displaystyle{4}{x}^{{2}}+{4}{x}-{4}\) are \(\displaystyle{x}=-{\frac{{{1}}}{{{2}}}}+{\frac{{\sqrt{{{5}}}}}{{{2}}}},-{\frac{{{1}}}{{{2}}}}-{\frac{{\sqrt{{{5}}}}}{{{2}}}}\)