P=(59x-0.3x^2)-(4x+14)

Solution for P=(59x-0.3x^2)-(4x+14) equation:

=(59P-0.3P^2)-(4P+14)

We move all terms to the left:

-((59P-0.3P^2)-(4P+14))=0


We calculate terms in parentheses: -((59P-0.3P^2)-(4P+14)), so:

(59P-0.3P^2)-(4P+14)

We get rid of parentheses

-0.3P^2+59P-4P-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+14=0

a = 0.3; b = -55; c = +14;
Δ = b2-4ac
Δ = -552-4·0.3·14
Δ = 3008.2
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{-(-55)-\sqrt{3008.2}}{2*0.3}=\frac{55-\sqrt{3008.2}}{0.6}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{3008.2}}{2*0.3}=\frac{55+\sqrt{3008.2}}{0.6}
$