P(x)=-0.4x^2+360x-(3x+4000)

Solution for P(x)=-0.4x^2+360x-(3x+4000) equation:

(P)=-0.4P^2+360P-(3P+4000)

We move all terms to the left:

(P)-(-0.4P^2+360P-(3P+4000))=0


We calculate terms in parentheses: -(-0.4P^2+360P-(3P+4000)), so:

-0.4P^2+360P-(3P+4000)

We get rid of parentheses

-0.4P^2+360P-3P-4000

We add all the numbers together, and all the variables

-0.4P^2+357P-4000

Back to the equation:

-(-0.4P^2+357P-4000)


We get rid of parentheses

0.4P^2-357P+P+4000=0

We add all the numbers together, and all the variables

0.4P^2-356P+4000=0

a = 0.4; b = -356; c = +4000;
Δ = b2-4ac
Δ = -3562-4·0.4·4000
Δ = 120336
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:

$\sqrt{\Delta}=\sqrt{120336}=\sqrt{16*7521}=\sqrt{16}*\sqrt{7521}=4\sqrt{7521}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-356)-4\sqrt{7521}}{2*0.4}=\frac{356-4\sqrt{7521}}{0.8}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-356)+4\sqrt{7521}}{2*0.4}=\frac{356+4\sqrt{7521}}{0.8}
$