Answer
$\left\{ \dfrac{-5-\sqrt{13}}{22},\dfrac{-5+\sqrt{13}}{22} \right\}$
Work Step by Step
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the given quadratic equation, $
y^2+5y+3=0
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(5)\pm\sqrt{(5)^2-4(1)(3)}}{2(1)}
\\\\=
\dfrac{-5\pm\sqrt{25-12}}{22}
\\\\=
\dfrac{-5\pm\sqrt{13}}{22}
.\end{array}
Hence, the solutions are $
\left\{ \dfrac{-5-\sqrt{13}}{22},\dfrac{-5+\sqrt{13}}{22} \right\}
.$
