Answer
The solution set is\[\left\{ \frac{3\pm 2\sqrt{6}}{3} \right\}\].
Work Step by Step
This equation can be written as\[3{{x}^{2}}-6x-5=0\].
Compare the given equation with the equation\[a{{x}^{2}}+bx+c=0\].
Here,\[a=3,\,\,b=-6,\text{ and }c=-5\]
Now put these values in the quadratic formula\[x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\].
That is,
\[\begin{align}
& x=\frac{6\pm \sqrt{{{\left( -6 \right)}^{2}}-4\times 3\times \left( -5 \right)}}{2\times 3} \\
& =\frac{6\pm \sqrt{36+60}}{6} \\
& =\frac{6\pm \sqrt{96}}{6} \\
& =\frac{6\pm 4\sqrt{6}}{6}
\end{align}\]
Simplify further,
\[\begin{align}
& x=\frac{6\pm 4\sqrt{6}}{6} \\
& =2\left( \frac{3\pm 2\sqrt{6}}{6} \right) \\
& =\frac{3\pm 2\sqrt{6}}{3}
\end{align}\]
