R(x)=-0.01x2+50x

Solution for R(x)=-0.01x2+50x equation:

(R)=-0.01R^2+50R

We move all terms to the left:

(R)-(-0.01R^2+50R)=0

We get rid of parentheses

0.01R^2-50R+R=0

We add all the numbers together, and all the variables

0.01R^2-49R=0

a = 0.01; b = -49; c = 0;
Δ = b2-4ac
Δ = -492-4·0.01·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-49}{2*0.01}=\frac{0}{0.02}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+49}{2*0.01}=\frac{98}{0.02}
=4900
$