P(x)=(60x-0.3x^2)

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

(P)=(60P-0.3P^2)

We move all terms to the left:

(P)-((60P-0.3P^2))=0


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

(60P-0.3P^2)

We get rid of parentheses

-0.3P^2+60P

Back to the equation:

-(-0.3P^2+60P)


We get rid of parentheses

0.3P^2-60P+P=0

We add all the numbers together, and all the variables

0.3P^2-59P=0

a = 0.3; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·0.3·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*0.3}=\frac{0}{0.6}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*0.3}=\frac{118}{0.6}
=196+0.40000000000001/0.6
$