P(x)=-0.04x(2)+240x-10000

Solution for P(x)=-0.04x(2)+240x-10000 equation:

(P)=-0.04P(2)+240P-10000

We move all terms to the left:

(P)-(-0.04P(2)+240P-10000)=0

We add all the numbers together, and all the variables

-(-0.04P^2+240P-10000)+P=0

We get rid of parentheses

0.04P^2-240P+P+10000=0

We add all the numbers together, and all the variables

0.04P^2-239P+10000=0

a = 0.04; b = -239; c = +10000;
Δ = b2-4ac
Δ = -2392-4·0.04·10000
Δ = 55521
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:

$\sqrt{\Delta}=\sqrt{55521}=\sqrt{9*6169}=\sqrt{9}*\sqrt{6169}=3\sqrt{6169}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-239)-3\sqrt{6169}}{2*0.04}=\frac{239-3\sqrt{6169}}{0.08}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-239)+3\sqrt{6169}}{2*0.04}=\frac{239+3\sqrt{6169}}{0.08}
$