R=800-0.05n2

Solution for R=800-0.05n2 equation:

=800-0.05R^2

We move all terms to the left:

-(800-0.05R^2)=0

We get rid of parentheses

0.05R^2-800=0

a = 0.05; b = 0; c = -800;
Δ = b2-4ac
Δ = 02-4·0.05·(-800)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*0.05}=\frac{0-4\sqrt{10}}{0.1}
=-\frac{4\sqrt{10}}{0.1}
=-\frac{\sqrt{10}}{0.025}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*0.05}=\frac{0+4\sqrt{10}}{0.1}
=\frac{4\sqrt{10}}{0.1}
=\frac{\sqrt{10}}{0.025}
$