3z^2-2z+6=0

Solution for 3z^2-2z+6=0 equation:

Simplifying
3z2 + -2z + 6 = 0

Reorder the terms:
6 + -2z + 3z2 = 0

Solving
6 + -2z + 3z2 = 0

Solving for variable 'z'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
2 + -0.6666666667z + z2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -0.6666666667z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + -0.6666666667z + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -0.6666666667z + z2 = 0 + -2
-0.6666666667z + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
-0.6666666667z + z2 = -2

The z term is -0.6666666667z.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667z + 0.1111111112 + z2 = -2 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667z + z2 = -2 + 0.1111111112

Combine like terms: -2 + 0.1111111112 = -1.8888888888
0.1111111112 + -0.6666666667z + z2 = -1.8888888888

Factor a perfect square on the left side:
(z + -0.3333333334)(z + -0.3333333334) = -1.8888888888

Can't calculate square root of the right side.

The solution to this equation could not be determined.