R(x)=8x-0.01x^2

Solution for R(x)=8x-0.01x^2 equation:

(R)=8R-0.01R^2

We move all terms to the left:

(R)-(8R-0.01R^2)=0

We get rid of parentheses

0.01R^2-8R+R=0

We add all the numbers together, and all the variables

0.01R^2-7R=0

a = 0.01; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·0.01·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*0.01}=\frac{0}{0.02}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*0.01}=\frac{14}{0.02}
=700
$