3y^2=-9y

Solution for 3y^2=-9y equation:

3y^2=-9y

We move all terms to the left:

3y^2-(-9y)=0

We get rid of parentheses

3y^2+9y=0

a = 3; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·3·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*3}=\frac{-18}{6}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*3}=\frac{0}{6}
=0
$