R(x)=35x-0.01x^2

Solution for R(x)=35x-0.01x^2 equation:

(R)=35R-0.01R^2

We move all terms to the left:

(R)-(35R-0.01R^2)=0

We get rid of parentheses

0.01R^2-35R+R=0

We add all the numbers together, and all the variables

0.01R^2-34R=0

a = 0.01; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·0.01·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*0.01}=\frac{0}{0.02}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*0.01}=\frac{68}{0.02}
=3400
$