(120-2x)(100-2x)=(2x)(x+10)

Solution for (120-2x)(100-2x)=(2x)(x+10) equation:

(120-2x)(100-2x)=(2x)(x+10)

We move all terms to the left:

(120-2x)(100-2x)-((2x)(x+10))=0

We add all the numbers together, and all the variables

(-2x+120)(-2x+100)-(2x(x+10))=0

We multiply parentheses ..

(+4x^2-200x-240x+12000)-(2x(x+10))=0


We calculate terms in parentheses: -(2x(x+10)), so:

2x(x+10)

We multiply parentheses

2x^2+20x

Back to the equation:

-(2x^2+20x)


We get rid of parentheses

4x^2-2x^2-200x-240x-20x+12000=0

We add all the numbers together, and all the variables

2x^2-460x+12000=0

a = 2; b = -460; c = +12000;
Δ = b2-4ac
Δ = -4602-4·2·12000
Δ = 115600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{115600}=340$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-460)-340}{2*2}=\frac{120}{4}
=30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-460)+340}{2*2}=\frac{800}{4}
=200
$