15y^2+12=-36y

Solution for 15y^2+12=-36y equation:

15y^2+12=-36y

We move all terms to the left:

15y^2+12-(-36y)=0

We get rid of parentheses

15y^2+36y+12=0

a = 15; b = 36; c = +12;
Δ = b2-4ac
Δ = 362-4·15·12
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-24}{2*15}=\frac{-60}{30}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+24}{2*15}=\frac{-12}{30}
=-2/5
$