0=3x^2-2x+6

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

Simplifying
0 = 3x2 + -2x + 6

Reorder the terms:
0 = 6 + -2x + 3x2

Solving
0 = 6 + -2x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + 2x + -3x2 = 6 + -2x + 3x2 + -6 + 2x + -3x2

Reorder the terms:
-6 + 2x + -3x2 = 6 + -6 + -2x + 2x + 3x2 + -3x2

Combine like terms: 6 + -6 = 0
-6 + 2x + -3x2 = 0 + -2x + 2x + 3x2 + -3x2
-6 + 2x + -3x2 = -2x + 2x + 3x2 + -3x2

Combine like terms: -2x + 2x = 0
-6 + 2x + -3x2 = 0 + 3x2 + -3x2
-6 + 2x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-6 + 2x + -3x2 = 0

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

Divide each side by '-3'.
2 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -0.6666666667x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -0.6666666667x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -0.6666666667x + x2 = 0 + -2
-0.6666666667x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-0.6666666667x + x2 = -2

The x term is -0.6666666667x.  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.
-0.6666666667x + 0.1111111112 + x2 = -2 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = -2 + 0.1111111112

Combine like terms: -2 + 0.1111111112 = -1.8888888888
0.1111111112 + -0.6666666667x + x2 = -1.8888888888

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

Can't calculate square root of the right side.

The solution to this equation could not be determined.