-6y(y+4)=-8y-36

Solution for -6y(y+4)=-8y-36 equation:

-6y(y+4)=-8y-36

We move all terms to the left:

-6y(y+4)-(-8y-36)=0

We multiply parentheses

-6y^2-24y-(-8y-36)=0

We get rid of parentheses

-6y^2-24y+8y+36=0

We add all the numbers together, and all the variables

-6y^2-16y+36=0

a = -6; b = -16; c = +36;
Δ = b2-4ac
Δ = -162-4·(-6)·36
Δ = 1120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{70}}{2*-6}=\frac{16-4\sqrt{70}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{70}}{2*-6}=\frac{16+4\sqrt{70}}{-12}
$