-9y(y+8)=3y-12

Solution for -9y(y+8)=3y-12 equation:

-9y(y+8)=3y-12

We move all terms to the left:

-9y(y+8)-(3y-12)=0

We multiply parentheses

-9y^2-72y-(3y-12)=0

We get rid of parentheses

-9y^2-72y-3y+12=0

We add all the numbers together, and all the variables

-9y^2-75y+12=0

a = -9; b = -75; c = +12;
Δ = b2-4ac
Δ = -752-4·(-9)·12
Δ = 6057
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:

$\sqrt{\Delta}=\sqrt{6057}=\sqrt{9*673}=\sqrt{9}*\sqrt{673}=3\sqrt{673}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-3\sqrt{673}}{2*-9}=\frac{75-3\sqrt{673}}{-18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+3\sqrt{673}}{2*-9}=\frac{75+3\sqrt{673}}{-18}
$