220=(12+2x)(16+2X)

Solution for 220=(12+2x)(16+2X) equation:

220=(12+2x)(16+2x)

We move all terms to the left:

220-((12+2x)(16+2x))=0

We add all the numbers together, and all the variables

-((2x+12)(2x+16))+220=0

We multiply parentheses ..

-((+4x^2+32x+24x+192))+220=0


We calculate terms in parentheses: -((+4x^2+32x+24x+192)), so:

(+4x^2+32x+24x+192)

We get rid of parentheses

4x^2+32x+24x+192

We add all the numbers together, and all the variables

4x^2+56x+192

Back to the equation:

-(4x^2+56x+192)


We get rid of parentheses

-4x^2-56x-192+220=0

We add all the numbers together, and all the variables

-4x^2-56x+28=0

a = -4; b = -56; c = +28;
Δ = b2-4ac
Δ = -562-4·(-4)·28
Δ = 3584
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:

$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-16\sqrt{14}}{2*-4}=\frac{56-16\sqrt{14}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+16\sqrt{14}}{2*-4}=\frac{56+16\sqrt{14}}{-8}
$