R(x)=11.5x-0.04x^2

Solution for R(x)=11.5x-0.04x^2 equation:

(R)=11.5R-0.04R^2

We move all terms to the left:

(R)-(11.5R-0.04R^2)=0

We get rid of parentheses

0.04R^2-11.5R+R=0

We add all the numbers together, and all the variables

0.04R^2-10.5R=0

a = 0.04; b = -10.5; c = 0;
Δ = b2-4ac
Δ = -10.52-4·0.04·0
Δ = 110.25
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{-(-10.5)-\sqrt{110.25}}{2*0.04}=\frac{10.5-\sqrt{110.25}}{0.08}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10.5)+\sqrt{110.25}}{2*0.04}=\frac{10.5+\sqrt{110.25}}{0.08}
$