P=80x-0.4x2-200

Solution for P=80x-0.4x2-200 equation:

=80P-0.4P^2-200

We move all terms to the left:

-(80P-0.4P^2-200)=0

We get rid of parentheses

0.4P^2-80P+200=0

a = 0.4; b = -80; c = +200;
Δ = b2-4ac
Δ = -802-4·0.4·200
Δ = 6080
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:

$\sqrt{\Delta}=\sqrt{6080}=\sqrt{64*95}=\sqrt{64}*\sqrt{95}=8\sqrt{95}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{95}}{2*0.4}=\frac{80-8\sqrt{95}}{0.8}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{95}}{2*0.4}=\frac{80+8\sqrt{95}}{0.8}
$