3x^2=13x-16

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Solution for 3x^2=13x-16 equation: 


Simplifying
3x2 = 13x + -16

Reorder the terms:
3x2 = -16 + 13x

Solving
3x2 = -16 + 13x

Solving for variable 'x'.

Reorder the terms:
16 + -13x + 3x2 = -16 + 13x + 16 + -13x

Reorder the terms:
16 + -13x + 3x2 = -16 + 16 + 13x + -13x

Combine like terms: -16 + 16 = 0
16 + -13x + 3x2 = 0 + 13x + -13x
16 + -13x + 3x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
16 + -13x + 3x2 = 0

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

Divide each side by '3'.
5.333333333 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + -4.333333333x + -5.333333333 + x2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + -4.333333333x + x2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + -4.333333333x + x2 = 0 + -5.333333333
-4.333333333x + x2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
-4.333333333x + x2 = -5.333333333

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = -5.333333333 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = -5.333333333 + 4.694444446

Combine like terms: -5.333333333 + 4.694444446 = -0.638888887
4.694444446 + -4.333333333x + x2 = -0.638888887

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = -0.638888887

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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