P=p(-2.5p+800)

Solution for P=p(-2.5p+800) equation:

=P(-2.5P+800)

We move all terms to the left:

-(P(-2.5P+800))=0


We calculate terms in parentheses: -(P(-2.5P+800)), so:

P(-2.5P+800)

We multiply parentheses

-2P^2+800P

Back to the equation:

-(-2P^2+800P)


We get rid of parentheses

2P^2-800P=0

a = 2; b = -800; c = 0;
Δ = b2-4ac
Δ = -8002-4·2·0
Δ = 640000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{640000}=800$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-800}{2*2}=\frac{0}{4}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+800}{2*2}=\frac{1600}{4}
=400
$