x=(400+20x)(90-x)

Solution for x=(400+20x)(90-x) equation:

x=(400+20x)(90-x)

We move all terms to the left:

x-((400+20x)(90-x))=0

We add all the numbers together, and all the variables

x-((20x+400)(-1x+90))=0

We multiply parentheses ..

-((-20x^2+1800x-400x+36000))+x=0


We calculate terms in parentheses: -((-20x^2+1800x-400x+36000)), so:

(-20x^2+1800x-400x+36000)

We get rid of parentheses

-20x^2+1800x-400x+36000

We add all the numbers together, and all the variables

-20x^2+1400x+36000

Back to the equation:

-(-20x^2+1400x+36000)


We get rid of parentheses

20x^2-1400x+x-36000=0

We add all the numbers together, and all the variables

20x^2-1399x-36000=0

a = 20; b = -1399; c = -36000;
Δ = b2-4ac
Δ = -13992-4·20·(-36000)
Δ = 4837201
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{-(-1399)-\sqrt{4837201}}{2*20}=\frac{1399-\sqrt{4837201}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1399)+\sqrt{4837201}}{2*20}=\frac{1399+\sqrt{4837201}}{40}
$