Answer
$\left\{ \dfrac{-\sqrt{7}-3\sqrt{7}}{2},\dfrac{-\sqrt{7}+3\sqrt{7}}{2} \right\}$
Work Step by Step
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the given quadratic equation, $
7x^2+\sqrt{7}x-2=0
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(\sqrt{7})\pm\sqrt{(\sqrt{7})^2-4(7)(-2)}}{2(1)}
\\\\=
\dfrac{-\sqrt{7}\pm\sqrt{7+56}}{2}
\\\\=
\dfrac{-\sqrt{7}\pm\sqrt{9\cdot7}}{2}
\\\\=
\dfrac{-\sqrt{7}\pm\sqrt{(3)^2\cdot7}}{2}
\\\\=
\dfrac{-\sqrt{7}\pm3\sqrt{7}}{2}
.\end{array}
Hence, the solutions are $
\left\{ \dfrac{-\sqrt{7}-3\sqrt{7}}{2},\dfrac{-\sqrt{7}+3\sqrt{7}}{2} \right\}
.$
