R(p)=-8p^2+40000

Solution for R(p)=-8p^2+40000 equation:

(R)=-8R^2+40000

We move all terms to the left:

(R)-(-8R^2+40000)=0

We get rid of parentheses

8R^2+R-40000=0

a = 8; b = 1; c = -40000;
Δ = b2-4ac
Δ = 12-4·8·(-40000)
Δ = 1280001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1280001}}{2*8}=\frac{-1-\sqrt{1280001}}{16}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1280001}}{2*8}=\frac{-1+\sqrt{1280001}}{16}
$