3x^2+20x+6=0

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Solution for 3x^2+20x+6=0 equation: 


Simplifying
3x2 + 20x + 6 = 0

Reorder the terms:
6 + 20x + 3x2 = 0

Solving
6 + 20x + 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 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 6.666666667x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 6.666666667x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 6.666666667x + x2 = 0 + -2
6.666666667x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
6.666666667x + x2 = -2

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = -2 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = -2 + 11.11111112

Combine like terms: -2 + 11.11111112 = 9.11111112
11.11111112 + 6.666666667x + x2 = 9.11111112

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 9.11111112

Calculate the square root of the right side: 3.018461714

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 3.018461714 and -3.018461714.


Subproblem 1
x + 3.333333334 = 3.018461714

Simplifying
x + 3.333333334 = 3.018461714

Reorder the terms:
3.333333334 + x = 3.018461714

Solving
3.333333334 + x = 3.018461714

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 3.018461714 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 3.018461714 + -3.333333334
x = 3.018461714 + -3.333333334

Combine like terms: 3.018461714 + -3.333333334 = -0.31487162
x = -0.31487162

Simplifying
x = -0.31487162


Subproblem 2
x + 3.333333334 = -3.018461714

Simplifying
x + 3.333333334 = -3.018461714

Reorder the terms:
3.333333334 + x = -3.018461714

Solving
3.333333334 + x = -3.018461714

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -3.018461714 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -3.018461714 + -3.333333334
x = -3.018461714 + -3.333333334

Combine like terms: -3.018461714 + -3.333333334 = -6.351795048
x = -6.351795048

Simplifying
x = -6.351795048


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.31487162, -6.351795048}

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