r(x)=200.000x-2000x2

Solution for r(x)=200.000x-2000x2 equation:

(R)=200.000R-2000R^2

We move all terms to the left:

(R)-(200.000R-2000R^2)=0

We get rid of parentheses

2000R^2-200.000R+R=0

We add all the numbers together, and all the variables

2000R^2-199R=0

a = 2000; b = -199; c = 0;
Δ = b2-4ac
Δ = -1992-4·2000·0
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*2000}=\frac{0}{4000}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-199)+199}{2*2000}=\frac{398}{4000}
=199/2000
$