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=3, b=−3 and c=−4

So,

\(\displaystyle{x}=\frac{{-{3}{\left(-{3}\right)}\pm\sqrt{{{\left(-{3}\right)}^{{2}}-{4}\times{3}\times{\left(-{4}\right)}}}}}{{{2}\times{3}}}\)

\(\displaystyle{x}=\frac{{{3}\pm\sqrt{{{9}+{48}}}}}{{6}}\)

\(\displaystyle{x}=\frac{{{3}\pm\sqrt{{57}}}}{{6}}\)

Therefore, solutions are

\(\displaystyle{x}=\frac{{{3}+\sqrt{{57}}}}{{6}}{\quad\text{and}\quad}{x}=\frac{{{3}-\sqrt{{57}}}}{{6}}\)

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

Here, a=3, b=−3 and c=−4

So,

\(\displaystyle{x}=\frac{{-{3}{\left(-{3}\right)}\pm\sqrt{{{\left(-{3}\right)}^{{2}}-{4}\times{3}\times{\left(-{4}\right)}}}}}{{{2}\times{3}}}\)

\(\displaystyle{x}=\frac{{{3}\pm\sqrt{{{9}+{48}}}}}{{6}}\)

\(\displaystyle{x}=\frac{{{3}\pm\sqrt{{57}}}}{{6}}\)

Therefore, solutions are

\(\displaystyle{x}=\frac{{{3}+\sqrt{{57}}}}{{6}}{\quad\text{and}\quad}{x}=\frac{{{3}-\sqrt{{57}}}}{{6}}\)