P=162x-81x2

Solution for P=162x-81x2 equation:

=162P-81P^2

We move all terms to the left:

-(162P-81P^2)=0

We get rid of parentheses

81P^2-162P=0

a = 81; b = -162; c = 0;
Δ = b2-4ac
Δ = -1622-4·81·0
Δ = 26244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26244}=162$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-162}{2*81}=\frac{0}{162}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+162}{2*81}=\frac{324}{162}
=2
$