P=-0.01x2+5000x-25000

Solution for P=-0.01x2+5000x-25000 equation:

=-0.01P^2+5000P-25000

We move all terms to the left:

-(-0.01P^2+5000P-25000)=0

We get rid of parentheses

0.01P^2-5000P+25000=0

a = 0.01; b = -5000; c = +25000;
Δ = b2-4ac
Δ = -50002-4·0.01·25000
Δ = 24999000
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:

$\sqrt{\Delta}=\sqrt{24999000}=\sqrt{100*249990}=\sqrt{100}*\sqrt{249990}=10\sqrt{249990}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5000)-10\sqrt{249990}}{2*0.01}=\frac{5000-10\sqrt{249990}}{0.02}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5000)+10\sqrt{249990}}{2*0.01}=\frac{5000+10\sqrt{249990}}{0.02}
$