3x^2=4x-5

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Solution for 3x^2=4x-5 equation: 


Simplifying
3x2 = 4x + -5

Reorder the terms:
3x2 = -5 + 4x

Solving
3x2 = -5 + 4x

Solving for variable 'x'.

Reorder the terms:
5 + -4x + 3x2 = -5 + 4x + 5 + -4x

Reorder the terms:
5 + -4x + 3x2 = -5 + 5 + 4x + -4x

Combine like terms: -5 + 5 = 0
5 + -4x + 3x2 = 0 + 4x + -4x
5 + -4x + 3x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
5 + -4x + 3x2 = 0

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

Divide each side by '3'.
1.666666667 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.333333333x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -1.333333333x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + -1.666666667
-1.333333333x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-1.333333333x + x2 = -1.666666667

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 = -1.666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = -1.666666667 + 0.4444444442

Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228
0.4444444442 + -1.333333333x + x2 = -1.2222222228

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = -1.2222222228

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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