Answer
$x=\dfrac{-5\pm\sqrt{17}}{4}$
Work Step by Step
Using the properties of equality, the given quadratic equation, $
2x^2=-5x-1
,$ is equivalent to
\begin{array}{l}\require{cancel}
2x^2+5x+1=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{-5\pm\sqrt{(5)^2-4(2)(1)}}{2(2)}
\\\\
x=\dfrac{-5\pm\sqrt{25-8}}{4}
\\\\
x=\dfrac{-5\pm\sqrt{17}}{4}
.\end{array}
