3x^2+36x+8=0

Solution for 3x^2+36x+8=0 equation:

Simplifying
3x2 + 36x + 8 = 0

Reorder the terms:
8 + 36x + 3x2 = 0

Solving
8 + 36x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
2.666666667 + 12x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + 12x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + 12x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + 12x + x2 = 0 + -2.666666667
12x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
12x + x2 = -2.666666667

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -2.666666667 + 36

Reorder the terms:
36 + 12x + x2 = -2.666666667 + 36

Combine like terms: -2.666666667 + 36 = 33.333333333
36 + 12x + x2 = 33.333333333

Factor a perfect square on the left side:
(x + 6)(x + 6) = 33.333333333

Calculate the square root of the right side: 5.773502692

Break this problem into two subproblems by setting 
(x + 6) equal to 5.773502692 and -5.773502692.

Subproblem 1
x + 6 = 5.773502692

Simplifying
x + 6 = 5.773502692

Reorder the terms:
6 + x = 5.773502692

Solving
6 + x = 5.773502692

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + x = 5.773502692 + -6

Combine like terms: 6 + -6 = 0
0 + x = 5.773502692 + -6
x = 5.773502692 + -6

Combine like terms: 5.773502692 + -6 = -0.226497308
x = -0.226497308

Simplifying
x = -0.226497308

Subproblem 2
x + 6 = -5.773502692

Simplifying
x + 6 = -5.773502692

Reorder the terms:
6 + x = -5.773502692

Solving
6 + x = -5.773502692

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + x = -5.773502692 + -6

Combine like terms: 6 + -6 = 0
0 + x = -5.773502692 + -6
x = -5.773502692 + -6

Combine like terms: -5.773502692 + -6 = -11.773502692
x = -11.773502692

Simplifying
x = -11.773502692

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.226497308, -11.773502692}