R(x)=1600x-4x^2

Solution for R(x)=1600x-4x^2 equation:

(R)=1600R-4R^2

We move all terms to the left:

(R)-(1600R-4R^2)=0

We get rid of parentheses

4R^2-1600R+R=0

We add all the numbers together, and all the variables

4R^2-1599R=0

a = 4; b = -1599; c = 0;
Δ = b2-4ac
Δ = -15992-4·4·0
Δ = 2556801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2556801}=1599$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1599)-1599}{2*4}=\frac{0}{8}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1599)+1599}{2*4}=\frac{3198}{8}
=399+3/4
$