(y+6)(y+3)=-2

Solution for (y+6)(y+3)=-2 equation:

(y+6)(y+3)=-2

We move all terms to the left:

(y+6)(y+3)-(-2)=0

We add all the numbers together, and all the variables

(y+6)(y+3)+2=0

We multiply parentheses ..

(+y^2+3y+6y+18)+2=0

We get rid of parentheses

y^2+3y+6y+18+2=0

We add all the numbers together, and all the variables

y^2+9y+20=0

a = 1; b = 9; c = +20;
Δ = b2-4ac
Δ = 92-4·1·20
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-1}{2*1}=\frac{-10}{2}
=-5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+1}{2*1}=\frac{-8}{2}
=-4
$