5y^2=-12y

Solution for 5y^2=-12y equation:

5y^2=-12y

We move all terms to the left:

5y^2-(-12y)=0

We get rid of parentheses

5y^2+12y=0

a = 5; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·5·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*5}=\frac{-24}{10}
=-2+2/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*5}=\frac{0}{10}
=0
$