X=650-5p-p^2

Solution for X=650-5p-p^2 equation:

X=650-5X-X^2

We move all terms to the left:

X-(650-5X-X^2)=0

We get rid of parentheses

X^2+5X+X-650=0

We add all the numbers together, and all the variables

X^2+6X-650=0

a = 1; b = 6; c = -650;
Δ = b2-4ac
Δ = 62-4·1·(-650)
Δ = 2636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2636}=\sqrt{4*659}=\sqrt{4}*\sqrt{659}=2\sqrt{659}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{659}}{2*1}=\frac{-6-2\sqrt{659}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{659}}{2*1}=\frac{-6+2\sqrt{659}}{2}
$