R=200x-0.4x^2

Solution for R=200x-0.4x^2 equation:

=200R-0.4R^2

We move all terms to the left:

-(200R-0.4R^2)=0

We get rid of parentheses

0.4R^2-200R=0

a = 0.4; b = -200; c = 0;
Δ = b2-4ac
Δ = -2002-4·0.4·0
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-200}{2*0.4}=\frac{0}{0.8}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+200}{2*0.4}=\frac{400}{0.8}
=500
$