P=(59x-0.4x^2)-(5x+15)

Solution for P=(59x-0.4x^2)-(5x+15) equation:

=(59P-0.4P^2)-(5P+15)

We move all terms to the left:

-((59P-0.4P^2)-(5P+15))=0


We calculate terms in parentheses: -((59P-0.4P^2)-(5P+15)), so:

(59P-0.4P^2)-(5P+15)

We get rid of parentheses

-0.4P^2+59P-5P-15

We add all the numbers together, and all the variables

-0.4P^2+54P-15

Back to the equation:

-(-0.4P^2+54P-15)


We get rid of parentheses

0.4P^2-54P+15=0

a = 0.4; b = -54; c = +15;
Δ = b2-4ac
Δ = -542-4·0.4·15
Δ = 2892
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:

$\sqrt{\Delta}=\sqrt{2892}=\sqrt{4*723}=\sqrt{4}*\sqrt{723}=2\sqrt{723}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{723}}{2*0.4}=\frac{54-2\sqrt{723}}{0.8}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{723}}{2*0.4}=\frac{54+2\sqrt{723}}{0.8}
$