R(x)=2x-0.02x^2

Solution for R(x)=2x-0.02x^2 equation:

(R)=2R-0.02R^2

We move all terms to the left:

(R)-(2R-0.02R^2)=0

We get rid of parentheses

0.02R^2-2R+R=0

We add all the numbers together, and all the variables

0.02R^2-1R=0

a = 0.02; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·0.02·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*0.02}=\frac{0}{0.04}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*0.02}=\frac{2}{0.04}
=50
$