Answer
$\left\{ \dfrac{-5-i\sqrt{5}}{10},\dfrac{-5+i\sqrt{5}}{10} \right\}$
Work Step by Step
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the given quadratic equation, $
10y^2+10y+3=0
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(10)\pm\sqrt{(10)^2-4(10)(3)}}{2(10)}
\\\\=
\dfrac{-10\pm\sqrt{100-120}}{20}
\\\\=
\dfrac{-10\pm\sqrt{-20}}{20}
\\\\=
\dfrac{-10\pm\sqrt{-1}\sqrt{20}}{20}
\\\\=
\dfrac{-10\pm i\sqrt{4\cdot5}}{20}
\\\\=
\dfrac{-10\pm i\sqrt{(2)^2\cdot5}}{20}
\\\\=
\dfrac{-10\pm 2i\sqrt{5}}{20}
\\\\=
\dfrac{2(-5\pm i\sqrt{5})}{20}
\\\\=
\dfrac{\cancel{2}(-5\pm i\sqrt{5})}{\cancel{2}\cdot10}
\\\\=
\dfrac{-5\pm i\sqrt{5}}{10}
.\end{array}
Hence, the solutions are $
\left\{ \dfrac{-5-i\sqrt{5}}{10},\dfrac{-5+i\sqrt{5}}{10} \right\}
.$
