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

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

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

We move all terms to the left:

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

We multiply parentheses

-8y^2+64y-(6y+36)=0

We get rid of parentheses

-8y^2+64y-6y-36=0

We add all the numbers together, and all the variables

-8y^2+58y-36=0

a = -8; b = 58; c = -36;
Δ = b2-4ac
Δ = 582-4·(-8)·(-36)
Δ = 2212
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:

$\sqrt{\Delta}=\sqrt{2212}=\sqrt{4*553}=\sqrt{4}*\sqrt{553}=2\sqrt{553}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-2\sqrt{553}}{2*-8}=\frac{-58-2\sqrt{553}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+2\sqrt{553}}{2*-8}=\frac{-58+2\sqrt{553}}{-16}
$