R(x)=13x-0.01x2

Solution for R(x)=13x-0.01x2 equation:

(R)=13R-0.01R^2

We move all terms to the left:

(R)-(13R-0.01R^2)=0

We get rid of parentheses

0.01R^2-13R+R=0

We add all the numbers together, and all the variables

0.01R^2-12R=0

a = 0.01; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·0.01·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*0.01}=\frac{0}{0.02}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*0.01}=\frac{24}{0.02}
=1200
$