(y+5)(y-1)=-8

Solution for (y+5)(y-1)=-8 equation:

(y+5)(y-1)=-8

We move all terms to the left:

(y+5)(y-1)-(-8)=0

We add all the numbers together, and all the variables

(y+5)(y-1)+8=0

We multiply parentheses ..

(+y^2-1y+5y-5)+8=0

We get rid of parentheses

y^2-1y+5y-5+8=0

We add all the numbers together, and all the variables

y^2+4y+3=0

a = 1; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·1·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2}{2*1}=\frac{-6}{2}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2}{2*1}=\frac{-2}{2}
=-1
$