R(x)=500x-0.001x^2

Solution for R(x)=500x-0.001x^2 equation:

(R)=500R-0.001R^2

We move all terms to the left:

(R)-(500R-0.001R^2)=0

We get rid of parentheses

0.001R^2-500R+R=0

We add all the numbers together, and all the variables

0.001R^2-499R=0

a = 0.001; b = -499; c = 0;
Δ = b2-4ac
Δ = -4992-4·0.001·0
Δ = 249001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{249001}=499$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-499)-499}{2*0.001}=\frac{0}{0.002}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-499)+499}{2*0.001}=\frac{998}{0.002}
=499000
$