5x^2+6x=12x-9

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Solution for 5x^2+6x=12x-9 equation: 


Simplifying
5x2 + 6x = 12x + -9

Reorder the terms:
6x + 5x2 = 12x + -9

Reorder the terms:
6x + 5x2 = -9 + 12x

Solving
6x + 5x2 = -9 + 12x

Solving for variable 'x'.

Reorder the terms:
9 + 6x + -12x + 5x2 = -9 + 12x + 9 + -12x

Combine like terms: 6x + -12x = -6x
9 + -6x + 5x2 = -9 + 12x + 9 + -12x

Reorder the terms:
9 + -6x + 5x2 = -9 + 9 + 12x + -12x

Combine like terms: -9 + 9 = 0
9 + -6x + 5x2 = 0 + 12x + -12x
9 + -6x + 5x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
9 + -6x + 5x2 = 0

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

Divide each side by '5'.
1.8 + -1.2x + x2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + -1.2x + -1.8 + x2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + -1.2x + x2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + -1.2x + x2 = 0 + -1.8
-1.2x + x2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
-1.2x + x2 = -1.8

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = -1.8 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = -1.8 + 0.36

Combine like terms: -1.8 + 0.36 = -1.44
0.36 + -1.2x + x2 = -1.44

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = -1.44

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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