Z3-z2-12z=0

Solution for Z3-z2-12z=0 equation:

3-Z2-12Z=0

We add all the numbers together, and all the variables

-1Z^2-12Z+3=0

a = -1; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·(-1)·3
Δ = 156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{39}}{2*-1}=\frac{12-2\sqrt{39}}{-2}
$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{39}}{2*-1}=\frac{12+2\sqrt{39}}{-2}
$