(y-6)(y+5)=-2

Solution for (y-6)(y+5)=-2 equation:

(y-6)(y+5)=-2

We move all terms to the left:

(y-6)(y+5)-(-2)=0

We add all the numbers together, and all the variables

(y-6)(y+5)+2=0

We multiply parentheses ..

(+y^2+5y-6y-30)+2=0

We get rid of parentheses

y^2+5y-6y-30+2=0

We add all the numbers together, and all the variables

y^2-1y-28=0

a = 1; b = -1; c = -28;
Δ = b2-4ac
Δ = -12-4·1·(-28)
Δ = 113
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{-(-1)-\sqrt{113}}{2*1}=\frac{1-\sqrt{113}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{113}}{2*1}=\frac{1+\sqrt{113}}{2}
$