Answer
$x=-\dfrac{5}{2}
\text{ and }
x=1
$
Work Step by Step
Using the properties of equality, the given equation, $
2x^2-5=-3x
,$ is equivalent to
\begin{align*}
2x^2+3x-5&=-3x+3x
\\
2x^2+3x-5&=0
\end{align*}
In the equation above, $a=
2
,$ $b=
3
,$ and $c=
-5
.$
Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}x&=
\dfrac{-3\pm\sqrt{3^2-4(2)(-5)}}{2(2)}
\\\\&=
\dfrac{-3\pm\sqrt{9+40}}{4}
\\\\&=
\dfrac{-3\pm\sqrt{49}}{4}
\\\\&=
\dfrac{-3\pm7}{4}
\end{align*}
\begin{array}{lcl}
&\Rightarrow
\dfrac{-3-7}{4} &\text{ OR }& \dfrac{-3+7}{4}
\\\\&
=\dfrac{-10}{4} && =\dfrac{4}{4}
\\\\&
=-\dfrac{5}{2} && =1
\end{array}
Hence, the solutions are $
x=-\dfrac{5}{2}
\text{ and }
x=1
.$
