2x+12=(x+20)(x+8)

Solution for 2x+12=(x+20)(x+8) equation:

2x+12=(x+20)(x+8)

We move all terms to the left:

2x+12-((x+20)(x+8))=0

We multiply parentheses ..

-((+x^2+8x+20x+160))+2x+12=0


We calculate terms in parentheses: -((+x^2+8x+20x+160)), so:

(+x^2+8x+20x+160)

We get rid of parentheses

x^2+8x+20x+160

We add all the numbers together, and all the variables

x^2+28x+160

Back to the equation:

-(x^2+28x+160)


We add all the numbers together, and all the variables

2x-(x^2+28x+160)+12=0

We get rid of parentheses

-x^2+2x-28x-160+12=0

We add all the numbers together, and all the variables

-1x^2-26x-148=0

a = -1; b = -26; c = -148;
Δ = b2-4ac
Δ = -262-4·(-1)·(-148)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{21}}{2*-1}=\frac{26-2\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{21}}{2*-1}=\frac{26+2\sqrt{21}}{-2}
$