(R)=-0.01x^2+1000x

Solution for (R)=-0.01x^2+1000x equation:

()=-0.01R^2+1000R

We move all terms to the left:

()-(-0.01R^2+1000R)=0

We add all the numbers together, and all the variables

-(-0.01R^2+1000R)=0

We get rid of parentheses

0.01R^2-1000R=0

a = 0.01; b = -1000; c = 0;
Δ = b2-4ac
Δ = -10002-4·0.01·0
Δ = 1000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1000000}=1000$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-1000}{2*0.01}=\frac{0}{0.02}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+1000}{2*0.01}=\frac{2000}{0.02}
=100000
$