R(x)=13.5x-0.05x^2

Solution for R(x)=13.5x-0.05x^2 equation:

(R)=13.5R-0.05R^2

We move all terms to the left:

(R)-(13.5R-0.05R^2)=0

We get rid of parentheses

0.05R^2-13.5R+R=0

We add all the numbers together, and all the variables

0.05R^2-12.5R=0

a = 0.05; b = -12.5; c = 0;
Δ = b2-4ac
Δ = -12.52-4·0.05·0
Δ = 156.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12.5)-\sqrt{156.25}}{2*0.05}=\frac{12.5-\sqrt{156.25}}{0.1}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12.5)+\sqrt{156.25}}{2*0.05}=\frac{12.5+\sqrt{156.25}}{0.1}
$