3x^2+8x+51=10

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Solution for 3x^2+8x+51=10 equation: 


Simplifying
3x2 + 8x + 51 = 10

Reorder the terms:
51 + 8x + 3x2 = 10

Solving
51 + 8x + 3x2 = 10

Solving for variable 'x'.

Reorder the terms:
51 + -10 + 8x + 3x2 = 10 + -10

Combine like terms: 51 + -10 = 41
41 + 8x + 3x2 = 10 + -10

Combine like terms: 10 + -10 = 0
41 + 8x + 3x2 = 0

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

Divide each side by '3'.
13.66666667 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '-13.66666667' to each side of the equation.
13.66666667 + 2.666666667x + -13.66666667 + x2 = 0 + -13.66666667

Reorder the terms:
13.66666667 + -13.66666667 + 2.666666667x + x2 = 0 + -13.66666667

Combine like terms: 13.66666667 + -13.66666667 = 0.00000000
0.00000000 + 2.666666667x + x2 = 0 + -13.66666667
2.666666667x + x2 = 0 + -13.66666667

Combine like terms: 0 + -13.66666667 = -13.66666667
2.666666667x + x2 = -13.66666667

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = -13.66666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = -13.66666667 + 1.777777780

Combine like terms: -13.66666667 + 1.777777780 = -11.88888889
1.777777780 + 2.666666667x + x2 = -11.88888889

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = -11.88888889

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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