P=-40x^2+140000x

Solution for P=-40x^2+140000x equation:

=-40P^2+140000P

We move all terms to the left:

-(-40P^2+140000P)=0

We get rid of parentheses

40P^2-140000P=0

a = 40; b = -140000; c = 0;
Δ = b2-4ac
Δ = -1400002-4·40·0
Δ = 19600000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600000000}=140000$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140000)-140000}{2*40}=\frac{0}{80}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140000)+140000}{2*40}=\frac{280000}{80}
=3500
$