x=(20-2x)(10-2x)

Solution for x=(20-2x)(10-2x) equation:

x=(20-2x)(10-2x)

We move all terms to the left:

x-((20-2x)(10-2x))=0

We add all the numbers together, and all the variables

x-((-2x+20)(-2x+10))=0

We multiply parentheses ..

-((+4x^2-20x-40x+200))+x=0


We calculate terms in parentheses: -((+4x^2-20x-40x+200)), so:

(+4x^2-20x-40x+200)

We get rid of parentheses

4x^2-20x-40x+200

We add all the numbers together, and all the variables

4x^2-60x+200

Back to the equation:

-(4x^2-60x+200)


We add all the numbers together, and all the variables

x-(4x^2-60x+200)=0

We get rid of parentheses

-4x^2+x+60x-200=0

We add all the numbers together, and all the variables

-4x^2+61x-200=0

a = -4; b = 61; c = -200;
Δ = b2-4ac
Δ = 612-4·(-4)·(-200)
Δ = 521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-\sqrt{521}}{2*-4}=\frac{-61-\sqrt{521}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+\sqrt{521}}{2*-4}=\frac{-61+\sqrt{521}}{-8}
$