100=(8+2x)(10+2x)

Solution for 100=(8+2x)(10+2x) equation:

100=(8+2x)(10+2x)

We move all terms to the left:

100-((8+2x)(10+2x))=0

We add all the numbers together, and all the variables

-((2x+8)(2x+10))+100=0

We multiply parentheses ..

-((+4x^2+20x+16x+80))+100=0


We calculate terms in parentheses: -((+4x^2+20x+16x+80)), so:

(+4x^2+20x+16x+80)

We get rid of parentheses

4x^2+20x+16x+80

We add all the numbers together, and all the variables

4x^2+36x+80

Back to the equation:

-(4x^2+36x+80)


We get rid of parentheses

-4x^2-36x-80+100=0

We add all the numbers together, and all the variables

-4x^2-36x+20=0

a = -4; b = -36; c = +20;
Δ = b2-4ac
Δ = -362-4·(-4)·20
Δ = 1616
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:

$\sqrt{\Delta}=\sqrt{1616}=\sqrt{16*101}=\sqrt{16}*\sqrt{101}=4\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{101}}{2*-4}=\frac{36-4\sqrt{101}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{101}}{2*-4}=\frac{36+4\sqrt{101}}{-8}
$