Answer
$y=-\dfrac{1}{2}\pm\dfrac{\sqrt{5}}{10}i$
Work Step by Step
$10y^{2}+10y+3=0$
Use the quadratic formula to solve this equation. The formula is $y=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=10$, $b=10$ and $c=3$
Substitute:
$y=\dfrac{-10\pm\sqrt{10^{2}-4(10)(3)}}{2(10)}=\dfrac{-10\pm\sqrt{100-120}}{20}=...$
$...=\dfrac{-10\pm\sqrt{-20}}{20}=\dfrac{-10\pm\sqrt{20}i}{20}=\dfrac{-10\pm2\sqrt{5}i}{20}=...$
$...=-\dfrac{1}{2}\pm\dfrac{\sqrt{5}}{10}i$