3x^2=4x-6

Solution for 3x^2=4x-6 equation:

Simplifying
3x2 = 4x + -6

Reorder the terms:
3x2 = -6 + 4x

Solving
3x2 = -6 + 4x

Solving for variable 'x'.

Reorder the terms:
6 + -4x + 3x2 = -6 + 4x + 6 + -4x

Reorder the terms:
6 + -4x + 3x2 = -6 + 6 + 4x + -4x

Combine like terms: -6 + 6 = 0
6 + -4x + 3x2 = 0 + 4x + -4x
6 + -4x + 3x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
6 + -4x + 3x2 = 0

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

Divide each side by '3'.
2 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1.333333333x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -1.333333333x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1.333333333x + x2 = 0 + -2
-1.333333333x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1.333333333x + x2 = -2

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = -2 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = -2 + 0.4444444442

Combine like terms: -2 + 0.4444444442 = -1.5555555558
0.4444444442 + -1.333333333x + x2 = -1.5555555558

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = -1.5555555558

Can't calculate square root of the right side.

The solution to this equation could not be determined.