(20+x)(500-20x)=R

Solution for (20+x)(500-20x)=R equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-20x^2+500x-400x+10000)=0

We get rid of parentheses

-20x^2+500x-400x+10000=0

We add all the numbers together, and all the variables

-20x^2+100x+10000=0

a = -20; b = 100; c = +10000;
Δ = b2-4ac
Δ = 1002-4·(-20)·10000
Δ = 810000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{810000}=900$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-900}{2*-20}=\frac{-1000}{-40}
=+25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+900}{2*-20}=\frac{800}{-40}
=-20
$