P(x)=52-0.3x^2-2x+16

Solution for P(x)=52-0.3x^2-2x+16 equation:

(P)=52-0.3P^2-2P+16

We move all terms to the left:

(P)-(52-0.3P^2-2P+16)=0

We get rid of parentheses

0.3P^2+2P+P-52-16=0

We add all the numbers together, and all the variables

0.3P^2+3P-68=0

a = 0.3; b = 3; c = -68;
Δ = b2-4ac
Δ = 32-4·0.3·(-68)
Δ = 90.6
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{-(3)-\sqrt{90.6}}{2*0.3}=\frac{-3-\sqrt{90.6}}{0.6}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{90.6}}{2*0.3}=\frac{-3+\sqrt{90.6}}{0.6}
$