R=800n-0.05n2

Solution for R=800n-0.05n2 equation:

=800R-0.05R^2

We move all terms to the left:

-(800R-0.05R^2)=0

We get rid of parentheses

0.05R^2-800R=0

a = 0.05; b = -800; c = 0;
Δ = b2-4ac
Δ = -8002-4·0.05·0
Δ = 640000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{640000}=800$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-800}{2*0.05}=\frac{0}{0.1}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+800}{2*0.05}=\frac{1600}{0.1}
=16000
$