Answer
$x=\dfrac{-3\pm\sqrt{19}}{5}$
Work Step by Step
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solutions of the given quadratic equation, $
5x^2+6x-2=0
,$ are
\begin{array}{l}\require{cancel}
x=\dfrac{-6\pm\sqrt{6^2-4(5)(-2)}}{2(5)}
\\\\
x=\dfrac{-6\pm\sqrt{36+40}}{10}
\\\\
x=\dfrac{-6\pm\sqrt{76}}{10}
\\\\
x=\dfrac{-6\pm\sqrt{4\cdot19}}{10}
\\\\
x=\dfrac{-6\pm\sqrt{(2)^2\cdot19}}{10}
\\\\
x=\dfrac{-6\pm2\sqrt{19}}{10}
\\\\
x=\dfrac{2(-3\pm\sqrt{19})}{10}
\\\\
x=\dfrac{\cancel{2}(-3\pm\sqrt{19})}{\cancel{2}(5)}
\\\\
x=\dfrac{-3\pm\sqrt{19}}{5}
.\end{array}
