z3-z2+9z-9=0

Solution for z3-z2+9z-9=0 equation:

3-Z2+9Z-9=0

We add all the numbers together, and all the variables

-1Z^2+9Z-6=0

a = -1; b = 9; c = -6;
Δ = b2-4ac
Δ = 92-4·(-1)·(-6)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{57}}{2*-1}=\frac{-9-\sqrt{57}}{-2}
$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{57}}{2*-1}=\frac{-9+\sqrt{57}}{-2}
$