R(p)=-4p^2+16000p

Solution for R(p)=-4p^2+16000p equation:

(R)=-4R^2+16000R

We move all terms to the left:

(R)-(-4R^2+16000R)=0

We get rid of parentheses

4R^2-16000R+R=0

We add all the numbers together, and all the variables

4R^2-15999R=0

a = 4; b = -15999; c = 0;
Δ = b2-4ac
Δ = -159992-4·4·0
Δ = 255968001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{255968001}=15999$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15999)-15999}{2*4}=\frac{0}{8}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15999)+15999}{2*4}=\frac{31998}{8}
=3999+3/4
$