P(x)=60x-6x2

Solution for P(x)=60x-6x2 equation:

(P)=60P-6P^2

We move all terms to the left:

(P)-(60P-6P^2)=0

We get rid of parentheses

6P^2-60P+P=0

We add all the numbers together, and all the variables

6P^2-59P=0

a = 6; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·6·0
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*6}=\frac{0}{12}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*6}=\frac{118}{12}
=9+5/6
$