12x^2+20x+51=0

Solution for 12x^2+20x+51=0 equation:

Simplifying
12x2 + 20x + 51 = 0

Reorder the terms:
51 + 20x + 12x2 = 0

Solving
51 + 20x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
4.25 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '-4.25' to each side of the equation.
4.25 + 1.666666667x + -4.25 + x2 = 0 + -4.25

Reorder the terms:
4.25 + -4.25 + 1.666666667x + x2 = 0 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + 1.666666667x + x2 = 0 + -4.25
1.666666667x + x2 = 0 + -4.25

Combine like terms: 0 + -4.25 = -4.25
1.666666667x + x2 = -4.25

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = -4.25 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = -4.25 + 0.6944444447

Combine like terms: -4.25 + 0.6944444447 = -3.5555555553
0.6944444447 + 1.666666667x + x2 = -3.5555555553

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = -3.5555555553

Can't calculate square root of the right side.

The solution to this equation could not be determined.