Answer
$x\approx-1.70
\text{ and }
x\approx4.70$
Work Step by Step
In the given equation,
\begin{align*}
x^2-3x-8=0
,\end{align*} $a=
1
,$ $b=
-3
,$ and $c=
-8
.$
Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}x&=
\dfrac{-(-3)\pm\sqrt{(-3)^2-4(1)(-8)}}{2(1)}
\\\\&=
\dfrac{3\pm\sqrt{9+32}}{2}
\\\\&=
\dfrac{3\pm\sqrt{41}}{2}
\end{align*}
\begin{array}{lcl}
&\Rightarrow
\dfrac{3-\sqrt{41}}{2} &\text{ OR }& \dfrac{3+\sqrt{41}}{2}
\\\\&
\approx-1.70 && \approx4.70
\end{array}
Hence, the solutions are $
x\approx-1.70
\text{ and }
x\approx4.70
.$
