3-6(z-2)z=-2

Solution for 3-6(z-2)z=-2 equation:

3-6(z-2)z=-2

We move all terms to the left:

3-6(z-2)z-(-2)=0

We add all the numbers together, and all the variables

-6(z-2)z+5=0

We multiply parentheses

-6z^2+12z+5=0

a = -6; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·(-6)·5
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{66}}{2*-6}=\frac{-12-2\sqrt{66}}{-12}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{66}}{2*-6}=\frac{-12+2\sqrt{66}}{-12}
$