Answer
$x\approx-0.19
\text{ and }
x\approx2.69$
Work Step by Step
Using the properties of equality, the given equation, $
2x^2-1=5x
,$ is equivalent to
\begin{align*}
2x^2-5x-1=0
\end{align*}
In the equation above, $a=
2
,$ $b=
-5
,$ and $c=
-1
.$
Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}x&=
\dfrac{-(-5)\pm\sqrt{(-5)^2-4(2)(-1)}}{2(2)}
\\\\&=
\dfrac{5\pm\sqrt{25+8}}{4}
\\\\&=
\dfrac{5\pm\sqrt{33}}{4}
\end{align*}
\begin{array}{lcl}
&\Rightarrow
\dfrac{5-\sqrt{33}}{4} &\text{ OR }& \dfrac{5+\sqrt{33}}{4}
\\\\&
\approx-0.19 && \approx2.69
\end{array}
Hence, the solutions are $
x\approx-0.19
\text{ and }
x\approx 2.69
.$
