Answer
$x=\left\{ -\dfrac{5}{2}, 1 \right\}$
Work Step by Step
Using the properties of equality, the given quadratic equation, $
2x^2+3x=5
,$ is equivalent to
\begin{array}{l}\require{cancel}
2x^2+3x-5=0
.\end{array}
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solutions of the quadratic equation above are
\begin{array}{l}\require{cancel}
x=\dfrac{-3\pm\sqrt{3^2-4(2)(-5)}}{2(2)}
\\\\
x=\dfrac{-3\pm\sqrt{9+40}}{4}
\\\\
x=\dfrac{-3\pm\sqrt{49}}{4}
\\\\
x=\dfrac{-3\pm7}{4}
\\\\
x=\left\{ -\dfrac{5}{2}, 1 \right\}
.\end{array}
