3(z-1)z+8=14

Solution for 3(z-1)z+8=14 equation:

3(z-1)z+8=14

We move all terms to the left:

3(z-1)z+8-(14)=0

We add all the numbers together, and all the variables

3(z-1)z-6=0

We multiply parentheses

3z^2-3z-6=0

a = 3; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·3·(-6)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*3}=\frac{-6}{6}
=-1
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*3}=\frac{12}{6}
=2
$