P(x)=3^3+9x^2-18x-24=0

Solution for P(x)=3^3+9x^2-18x-24=0 equation:

(P)=3^3+9P^2-18P-24=0

We move all terms to the left:

(P)-(3^3+9P^2-18P-24)=0

We get rid of parentheses

-9P^2+18P+P+24-3^3=0

We add all the numbers together, and all the variables

-9P^2+19P-3=0

a = -9; b = 19; c = -3;
Δ = b2-4ac
Δ = 192-4·(-9)·(-3)
Δ = 253
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{-(19)-\sqrt{253}}{2*-9}=\frac{-19-\sqrt{253}}{-18}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{253}}{2*-9}=\frac{-19+\sqrt{253}}{-18}
$