P(x)=-0.3x^2+48x+8

Solution for P(x)=-0.3x^2+48x+8 equation:

(P)=-0.3P^2+48P+8

We move all terms to the left:

(P)-(-0.3P^2+48P+8)=0

We get rid of parentheses

0.3P^2-48P+P-8=0

We add all the numbers together, and all the variables

0.3P^2-47P-8=0

a = 0.3; b = -47; c = -8;
Δ = b2-4ac
Δ = -472-4·0.3·(-8)
Δ = 2218.6
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{-(-47)-\sqrt{2218.6}}{2*0.3}=\frac{47-\sqrt{2218.6}}{0.6}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{2218.6}}{2*0.3}=\frac{47+\sqrt{2218.6}}{0.6}
$