(y-5)(y+8)=8

Solution for (y-5)(y+8)=8 equation:

(y-5)(y+8)=8

We move all terms to the left:

(y-5)(y+8)-(8)=0

We multiply parentheses ..

(+y^2+8y-5y-40)-8=0

We get rid of parentheses

y^2+8y-5y-40-8=0

We add all the numbers together, and all the variables

y^2+3y-48=0

a = 1; b = 3; c = -48;
Δ = b2-4ac
Δ = 32-4·1·(-48)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{201}}{2*1}=\frac{-3-\sqrt{201}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{201}}{2*1}=\frac{-3+\sqrt{201}}{2}
$