(X+8)(x+4)=-2

Solution for (X+8)(x+4)=-2 equation:

(X+8)(X+4)=-2

We move all terms to the left:

(X+8)(X+4)-(-2)=0

We add all the numbers together, and all the variables

(X+8)(X+4)+2=0

We multiply parentheses ..

(+X^2+4X+8X+32)+2=0

We get rid of parentheses

X^2+4X+8X+32+2=0

We add all the numbers together, and all the variables

X^2+12X+34=0

a = 1; b = 12; c = +34;
Δ = b2-4ac
Δ = 122-4·1·34
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{2}}{2*1}=\frac{-12-2\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{2}}{2*1}=\frac{-12+2\sqrt{2}}{2}
$