Answer
$y=-1\pm\dfrac{\sqrt{6}}{3}i$
Work Step by Step
$3y^{2}+6y+5=0$
Use the quadratic formula to solve this equation. The formula is $y=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=3$, $b=6$ and $c=5$.
Substitute:
$y=\dfrac{-6\pm\sqrt{6^{2}-4(3)(5)}}{2(3)}=\dfrac{-6\pm\sqrt{36-60}}{6}=...$
$...=\dfrac{-6\pm\sqrt{-24}}{6}=\dfrac{-6\pm\sqrt{24}i}{6}=\dfrac{-6\pm2\sqrt{6}i}{6}=...$
$...=-1\pm\dfrac{\sqrt{6}}{3}i$
