Answer
$x\approx-2.49
\text{ and }
x\approx0.89$
Work Step by Step
In the given equation,
\begin{align*}
5x^2+8x-11=0
,\end{align*} $a=
5
,$ $b=
8
,$ and $c=
-11
.$
Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}x&=
\dfrac{-8\pm\sqrt{8^2-4(5)(-11)}}{2(5)}
\\\\&=
\dfrac{-8\pm\sqrt{64-220}}{10}
\\\\&=
\dfrac{-8\pm\sqrt{284}}{10}
\\\\&=
\dfrac{-8\pm\sqrt{4\cdot71}}{10}
\\\\&=
\dfrac{-8\pm2\sqrt{71}}{10}
\\\\&=
\dfrac{-\cancel8^4\pm\cancel2\sqrt{71}}{\cancel{10}^5}
&\text{ (divide by $2$)}
\\\\&=
\dfrac{-4\pm\sqrt{71}}{5}
\end{align*}
\begin{array}{lcl}
&\Rightarrow
\dfrac{-4-\sqrt{71}}{5} &\text{ OR }& \dfrac{-4+\sqrt{71}}{5}
\\\\&
\approx-2.49 && \approx0.89
\end{array}
Hence, the solutions are $
x\approx-2.49
\text{ and }
x\approx0.89
.$
