Z^3-3z^2+3z=1

Solution for Z^3-3z^2+3z=1 equation:

^3-3Z^2+3Z=1

We move all terms to the left:

^3-3Z^2+3Z-(1)=0

determiningTheFunctionDomain
-3Z^2+3Z-1+^3=0

We add all the numbers together, and all the variables

-3Z^2+3Z=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:
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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