P=18x-0.2x^2-100

Solution for P=18x-0.2x^2-100 equation:

=18P-0.2P^2-100

We move all terms to the left:

-(18P-0.2P^2-100)=0

We get rid of parentheses

0.2P^2-18P+100=0

a = 0.2; b = -18; c = +100;
Δ = b2-4ac
Δ = -182-4·0.2·100
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{61}}{2*0.2}=\frac{18-2\sqrt{61}}{0.4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{61}}{2*0.2}=\frac{18+2\sqrt{61}}{0.4}
$