(2x+4)(x+8)=-12

Solution for (2x+4)(x+8)=-12 equation:

(2x+4)(x+8)=-12

We move all terms to the left:

(2x+4)(x+8)-(-12)=0

We add all the numbers together, and all the variables

(2x+4)(x+8)+12=0

We multiply parentheses ..

(+2x^2+16x+4x+32)+12=0

We get rid of parentheses

2x^2+16x+4x+32+12=0

We add all the numbers together, and all the variables

2x^2+20x+44=0

a = 2; b = 20; c = +44;
Δ = b2-4ac
Δ = 202-4·2·44
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{3}}{2*2}=\frac{-20-4\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{3}}{2*2}=\frac{-20+4\sqrt{3}}{4}
$