Answer
The solution set of the equation $5{{x}^{2}}-6x-8=0$ is $\left\{ -\frac{4}{5},2 \right\}$.
Work Step by Step
Consider the equation, $5{{x}^{2}}-6x-8=0$
Compare the equation $5{{x}^{2}}-6x-8=0$ with the equation $a{{x}^{2}}+bx+c=0$ to find the values of $a$, $b$ and $c$.
$\begin{align}
& a=5 \\
& b=-6 \\
& c=-8 \\
\end{align}$
Substitute $a=5$, $b=-6$ and $c=-8$ in the equation $x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$.
$\begin{align}
& x=\frac{-\left( -6 \right)\pm \sqrt{{{\left( -6 \right)}^{2}}-4\left( 5 \right)\left( -8 \right)}}{2\left( 5 \right)} \\
& =\frac{6\pm \sqrt{36+160}}{10} \\
& =\frac{6\pm \sqrt{196}}{10} \\
& =\frac{6\pm 14}{10}
\end{align}$
Further solve the equation.
$\begin{align}
& x=\frac{6-14}{10}\text{ or }x=\frac{6+14}{10} \\
& x=-\frac{8}{10}\text{ or }x=\frac{20}{10} \\
& x=-\frac{4}{5}\text{ or }x=2 \\
\end{align}$
Therefore, the solution set of the equation $5{{x}^{2}}-6x-8=0$ is $\left\{ -\frac{4}{5},2 \right\}$.
