7x^2+12x+3=0

Solution for 7x^2+12x+3=0 equation:

Simplifying
7x2 + 12x + 3 = 0

Reorder the terms:
3 + 12x + 7x2 = 0

Solving
3 + 12x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
0.4285714286 + 1.714285714x + x2 = 0

Move the constant term to the right:

Add '-0.4285714286' to each side of the equation.
0.4285714286 + 1.714285714x + -0.4285714286 + x2 = 0 + -0.4285714286

Reorder the terms:
0.4285714286 + -0.4285714286 + 1.714285714x + x2 = 0 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + 1.714285714x + x2 = 0 + -0.4285714286
1.714285714x + x2 = 0 + -0.4285714286

Combine like terms: 0 + -0.4285714286 = -0.4285714286
1.714285714x + x2 = -0.4285714286

The x term is 1.714285714x.  Take half its coefficient (0.857142857).
Square it (0.7346938773) and add it to both sides.

Add '0.7346938773' to each side of the equation.
1.714285714x + 0.7346938773 + x2 = -0.4285714286 + 0.7346938773

Reorder the terms:
0.7346938773 + 1.714285714x + x2 = -0.4285714286 + 0.7346938773

Combine like terms: -0.4285714286 + 0.7346938773 = 0.3061224487
0.7346938773 + 1.714285714x + x2 = 0.3061224487

Factor a perfect square on the left side:
(x + 0.857142857)(x + 0.857142857) = 0.3061224487

Calculate the square root of the right side: 0.553283335

Break this problem into two subproblems by setting 
(x + 0.857142857) equal to 0.553283335 and -0.553283335.

Subproblem 1
x + 0.857142857 = 0.553283335

Simplifying
x + 0.857142857 = 0.553283335

Reorder the terms:
0.857142857 + x = 0.553283335

Solving
0.857142857 + x = 0.553283335

Solving for variable 'x'.

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

Add '-0.857142857' to each side of the equation.
0.857142857 + -0.857142857 + x = 0.553283335 + -0.857142857

Combine like terms: 0.857142857 + -0.857142857 = 0.000000000
0.000000000 + x = 0.553283335 + -0.857142857
x = 0.553283335 + -0.857142857

Combine like terms: 0.553283335 + -0.857142857 = -0.303859522
x = -0.303859522

Simplifying
x = -0.303859522

Subproblem 2
x + 0.857142857 = -0.553283335

Simplifying
x + 0.857142857 = -0.553283335

Reorder the terms:
0.857142857 + x = -0.553283335

Solving
0.857142857 + x = -0.553283335

Solving for variable 'x'.

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

Add '-0.857142857' to each side of the equation.
0.857142857 + -0.857142857 + x = -0.553283335 + -0.857142857

Combine like terms: 0.857142857 + -0.857142857 = 0.000000000
0.000000000 + x = -0.553283335 + -0.857142857
x = -0.553283335 + -0.857142857

Combine like terms: -0.553283335 + -0.857142857 = -1.410426192
x = -1.410426192

Simplifying
x = -1.410426192

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.303859522, -1.410426192}