P(x)=-2x^2+2x+800

Solution for P(x)=-2x^2+2x+800 equation:

(P)=-2P^2+2P+800

We move all terms to the left:

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

We get rid of parentheses

2P^2-2P+P-800=0

We add all the numbers together, and all the variables

2P^2-1P-800=0

a = 2; b = -1; c = -800;
Δ = b2-4ac
Δ = -12-4·2·(-800)
Δ = 6401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{6401}}{2*2}=\frac{1-\sqrt{6401}}{4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{6401}}{2*2}=\frac{1+\sqrt{6401}}{4}
$