0=3x^2-x+6

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

Simplifying
0 = 3x2 + -1x + 6

Reorder the terms:
0 = 6 + -1x + 3x2

Solving
0 = 6 + -1x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + x + -3x2 = 6 + -1x + 3x2 + -6 + x + -3x2

Reorder the terms:
-6 + x + -3x2 = 6 + -6 + -1x + x + 3x2 + -3x2

Combine like terms: 6 + -6 = 0
-6 + x + -3x2 = 0 + -1x + x + 3x2 + -3x2
-6 + x + -3x2 = -1x + x + 3x2 + -3x2

Combine like terms: -1x + x = 0
-6 + x + -3x2 = 0 + 3x2 + -3x2
-6 + x + -3x2 = 3x2 + -3x2

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

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

Divide each side by '-3'.
2 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -0.3333333333x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -0.3333333333x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -0.3333333333x + x2 = 0 + -2
-0.3333333333x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-0.3333333333x + x2 = -2

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.3333333333x + 0.25 + x2 = -2 + 0.25

Reorder the terms:
0.25 + -0.3333333333x + x2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + -0.3333333333x + x2 = -1.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.