P(x)=-0.0004x^2+2.4x-400

Solution for P(x)=-0.0004x^2+2.4x-400 equation:

(P)=-0.0004P^2+2.4P-400

We move all terms to the left:

(P)-(-0.0004P^2+2.4P-400)=0

We get rid of parentheses

0.0004P^2-2.4P+P+400=0

We add all the numbers together, and all the variables

0.0004P^2-1.4P+400=0

a = 0.0004; b = -1.4; c = +400;
Δ = b2-4ac
Δ = -1.42-4·0.0004·400
Δ = 1.32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.4)-\sqrt{1.32}}{2*0.0004}=\frac{1.4-\sqrt{1.32}}{0.0008}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.4)+\sqrt{1.32}}{2*0.0004}=\frac{1.4+\sqrt{1.32}}{0.0008}
$