11000=(20-x)*(500+50x)

Solution for 11000=(20-x)*(500+50x) equation:

11000=(20-x)(500+50x)

We move all terms to the left:

11000-((20-x)(500+50x))=0

We add all the numbers together, and all the variables

-((-1x+20)(50x+500))+11000=0

We multiply parentheses ..

-((-50x^2-500x+1000x+10000))+11000=0


We calculate terms in parentheses: -((-50x^2-500x+1000x+10000)), so:

(-50x^2-500x+1000x+10000)

We get rid of parentheses

-50x^2-500x+1000x+10000

We add all the numbers together, and all the variables

-50x^2+500x+10000

Back to the equation:

-(-50x^2+500x+10000)


We get rid of parentheses

50x^2-500x-10000+11000=0

We add all the numbers together, and all the variables

50x^2-500x+1000=0

a = 50; b = -500; c = +1000;
Δ = b2-4ac
Δ = -5002-4·50·1000
Δ = 50000
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:

$\sqrt{\Delta}=\sqrt{50000}=\sqrt{10000*5}=\sqrt{10000}*\sqrt{5}=100\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-100\sqrt{5}}{2*50}=\frac{500-100\sqrt{5}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+100\sqrt{5}}{2*50}=\frac{500+100\sqrt{5}}{100}
$