P^3-3p^2-3p+1=0

Solution for P^3-3p^2-3p+1=0 equation:

^3-3P^2-3P+1=0

We add all the numbers together, and all the variables

-3P^2-3P=0

a = -3; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-3)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-3}=\frac{0}{-6}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-3}=\frac{6}{-6}
=-1
$