D(15)=2115-2p-p^2

Solution for D(15)=2115-2p-p^2 equation:

(15)=2115-2D-D^2

We move all terms to the left:

(15)-(2115-2D-D^2)=0

We get rid of parentheses

D^2+2D-2115+15=0

We add all the numbers together, and all the variables

D^2+2D-2100=0

a = 1; b = 2; c = -2100;
Δ = b2-4ac
Δ = 22-4·1·(-2100)
Δ = 8404
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:

$\sqrt{\Delta}=\sqrt{8404}=\sqrt{4*2101}=\sqrt{4}*\sqrt{2101}=2\sqrt{2101}$
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{2101}}{2*1}=\frac{-2-2\sqrt{2101}}{2}
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{2101}}{2*1}=\frac{-2+2\sqrt{2101}}{2}
$