Answer
$\dfrac{-\sqrt{5}}{3} \text{ }$
Work Step by Step
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the given quadratic equation, $
5x^2+\sqrt{20}x+1=0
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(\sqrt{20})\pm\sqrt{(\sqrt{20})^2-4(5)(1)}}{2(3)}
\\\\=
\dfrac{-\sqrt{20}\pm\sqrt{20-20}}{6}
\\\\=
\dfrac{-\sqrt{20}\pm\sqrt{0}}{6}
\\\\=
\dfrac{-\sqrt{20}\pm0}{6}
\\\\=
\dfrac{-\sqrt{20}}{6}
\\\\=
\dfrac{-\sqrt{4\cdot5}}{6}
\\\\=
\dfrac{-\sqrt{(2)^2\cdot5}}{6}
\\\\=
\dfrac{-2\sqrt{5}}{6}
\\\\=
\dfrac{-\cancel{2}\sqrt{5}}{\cancel{2}\cdot3}
\\\\=
\dfrac{-\sqrt{5}}{3}
.\end{array}
Hence, the solutions are $
\dfrac{-\sqrt{5}}{3} \text{ }
.$
