1600=(20+2x)(40+2x)

Solution for 1600=(20+2x)(40+2x) equation:

1600=(20+2x)(40+2x)

We move all terms to the left:

1600-((20+2x)(40+2x))=0

We add all the numbers together, and all the variables

-((2x+20)(2x+40))+1600=0

We multiply parentheses ..

-((+4x^2+80x+40x+800))+1600=0


We calculate terms in parentheses: -((+4x^2+80x+40x+800)), so:

(+4x^2+80x+40x+800)

We get rid of parentheses

4x^2+80x+40x+800

We add all the numbers together, and all the variables

4x^2+120x+800

Back to the equation:

-(4x^2+120x+800)


We get rid of parentheses

-4x^2-120x-800+1600=0

We add all the numbers together, and all the variables

-4x^2-120x+800=0

a = -4; b = -120; c = +800;
Δ = b2-4ac
Δ = -1202-4·(-4)·800
Δ = 27200
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:

$\sqrt{\Delta}=\sqrt{27200}=\sqrt{1600*17}=\sqrt{1600}*\sqrt{17}=40\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-40\sqrt{17}}{2*-4}=\frac{120-40\sqrt{17}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+40\sqrt{17}}{2*-4}=\frac{120+40\sqrt{17}}{-8}
$