R(x)=200x-x^2

Solution for R(x)=200x-x^2 equation:

(R)=200R-R^2

We move all terms to the left:

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

We get rid of parentheses

R^2-200R+R=0

We add all the numbers together, and all the variables

R^2-199R=0

a = 1; b = -199; c = 0;
Δ = b2-4ac
Δ = -1992-4·1·0
Δ = 39601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39601}=199$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-199)-199}{2*1}=\frac{0}{2}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-199)+199}{2*1}=\frac{398}{2}
=199
$