R=90n-0.05n^2

Solution for R=90n-0.05n^2 equation:

=90R-0.05R^2

We move all terms to the left:

-(90R-0.05R^2)=0

We get rid of parentheses

0.05R^2-90R=0

a = 0.05; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·0.05·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90}{2*0.05}=\frac{0}{0.1}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*0.05}=\frac{180}{0.1}
=1800
$