6x^2=4x-9

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Solution for 6x^2=4x-9 equation:


Simplifying
6x2 = 4x + -9

Reorder the terms:
6x2 = -9 + 4x

Solving
6x2 = -9 + 4x

Solving for variable 'x'.

Reorder the terms:
9 + -4x + 6x2 = -9 + 4x + 9 + -4x

Reorder the terms:
9 + -4x + 6x2 = -9 + 9 + 4x + -4x

Combine like terms: -9 + 9 = 0
9 + -4x + 6x2 = 0 + 4x + -4x
9 + -4x + 6x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
9 + -4x + 6x2 = 0

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

Divide each side by '6'.
1.5 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -0.6666666667x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -0.6666666667x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -0.6666666667x + x2 = 0 + -1.5
-0.6666666667x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-0.6666666667x + x2 = -1.5

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 = -1.5 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = -1.5 + 0.1111111112

Combine like terms: -1.5 + 0.1111111112 = -1.3888888888
0.1111111112 + -0.6666666667x + x2 = -1.3888888888

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = -1.3888888888

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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