R(p)=-8p^2+16000p

Solution for R(p)=-8p^2+16000p equation:

(R)=-8R^2+16000R

We move all terms to the left:

(R)-(-8R^2+16000R)=0

We get rid of parentheses

8R^2-16000R+R=0

We add all the numbers together, and all the variables

8R^2-15999R=0

a = 8; b = -15999; c = 0;
Δ = b2-4ac
Δ = -159992-4·8·0
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*8}=\frac{0}{16}
=0
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15999)+15999}{2*8}=\frac{31998}{16}
=1999+7/8
$