P=200+800x+-1x2

Solution for P=200+800x+-1x2 equation:

=200+800P+-1P^2

We move all terms to the left:

-(200+800P+-1P^2)=0

We use the square of the difference formula

-(200+800P-1P^2)=0

We get rid of parentheses

1P^2-800P-200=0

We add all the numbers together, and all the variables

P^2-800P-200=0

a = 1; b = -800; c = -200;
Δ = b2-4ac
Δ = -8002-4·1·(-200)
Δ = 640800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{640800}=\sqrt{3600*178}=\sqrt{3600}*\sqrt{178}=60\sqrt{178}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-60\sqrt{178}}{2*1}=\frac{800-60\sqrt{178}}{2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+60\sqrt{178}}{2*1}=\frac{800+60\sqrt{178}}{2}
$