P(x)=(60x-0.3x^2)-(5x+15)

Solution for P(x)=(60x-0.3x^2)-(5x+15) equation:

(P)=(60P-0.3P^2)-(5P+15)

We move all terms to the left:

(P)-((60P-0.3P^2)-(5P+15))=0


We calculate terms in parentheses: -((60P-0.3P^2)-(5P+15)), so:

(60P-0.3P^2)-(5P+15)

We get rid of parentheses

-0.3P^2+60P-5P-15

We add all the numbers together, and all the variables

-0.3P^2+55P-15

Back to the equation:

-(-0.3P^2+55P-15)


We get rid of parentheses

0.3P^2-55P+P+15=0

We add all the numbers together, and all the variables

0.3P^2-54P+15=0

a = 0.3; b = -54; c = +15;
Δ = b2-4ac
Δ = -542-4·0.3·15
Δ = 2898
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:

$\sqrt{\Delta}=\sqrt{2898}=\sqrt{9*322}=\sqrt{9}*\sqrt{322}=3\sqrt{322}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-3\sqrt{322}}{2*0.3}=\frac{54-3\sqrt{322}}{0.6}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+3\sqrt{322}}{2*0.3}=\frac{54+3\sqrt{322}}{0.6}
$