D(p)=2000-4p-p2

Solution for D(p)=2000-4p-p2 equation:

(D)=2000-4D-D2

We move all terms to the left:

(D)-(2000-4D-D2)=0

We add all the numbers together, and all the variables

-(-4D-1D^2+2000)+D=0

We get rid of parentheses

1D^2+4D+D-2000=0

We add all the numbers together, and all the variables

D^2+5D-2000=0

a = 1; b = 5; c = -2000;
Δ = b2-4ac
Δ = 52-4·1·(-2000)
Δ = 8025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8025}=\sqrt{25*321}=\sqrt{25}*\sqrt{321}=5\sqrt{321}$
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{321}}{2*1}=\frac{-5-5\sqrt{321}}{2}
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{321}}{2*1}=\frac{-5+5\sqrt{321}}{2}
$