R(100)=36x-0.01x^2

Solution for R(100)=36x-0.01x^2 equation:

(100)=36R-0.01R^2

We move all terms to the left:

(100)-(36R-0.01R^2)=0

We get rid of parentheses

0.01R^2-36R+100=0

a = 0.01; b = -36; c = +100;
Δ = b2-4ac
Δ = -362-4·0.01·100
Δ = 1292
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1292}=\sqrt{4*323}=\sqrt{4}*\sqrt{323}=2\sqrt{323}$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{323}}{2*0.01}=\frac{36-2\sqrt{323}}{0.02}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{323}}{2*0.01}=\frac{36+2\sqrt{323}}{0.02}
$