P(x)=(60x-0.3x^2)-(5x+14)

Solution for P(x)=(60x-0.3x^2)-(5x+14) equation:

(P)=(60P-0.3P^2)-(5P+14)

We move all terms to the left:

(P)-((60P-0.3P^2)-(5P+14))=0


We calculate terms in parentheses: -((60P-0.3P^2)-(5P+14)), so:

(60P-0.3P^2)-(5P+14)

We get rid of parentheses

-0.3P^2+60P-5P-14

We add all the numbers together, and all the variables

-0.3P^2+55P-14

Back to the equation:

-(-0.3P^2+55P-14)


We get rid of parentheses

0.3P^2-55P+P+14=0

We add all the numbers together, and all the variables

0.3P^2-54P+14=0

a = 0.3; b = -54; c = +14;
Δ = b2-4ac
Δ = -542-4·0.3·14
Δ = 2899.2
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{-(-54)-\sqrt{2899.2}}{2*0.3}=\frac{54-\sqrt{2899.2}}{0.6}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+\sqrt{2899.2}}{2*0.3}=\frac{54+\sqrt{2899.2}}{0.6}
$