12x^2-38x+3=0

Solution for 12x^2-38x+3=0 equation:

Simplifying
12x2 + -38x + 3 = 0

Reorder the terms:
3 + -38x + 12x2 = 0

Solving
3 + -38x + 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'.
0.25 + -3.166666667x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -3.166666667x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -3.166666667x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -3.166666667x + x2 = 0 + -0.25
-3.166666667x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-3.166666667x + x2 = -0.25

The x term is -3.166666667x.  Take half its coefficient (-1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
-3.166666667x + 2.506944447 + x2 = -0.25 + 2.506944447

Reorder the terms:
2.506944447 + -3.166666667x + x2 = -0.25 + 2.506944447

Combine like terms: -0.25 + 2.506944447 = 2.256944447
2.506944447 + -3.166666667x + x2 = 2.256944447

Factor a perfect square on the left side:
(x + -1.583333334)(x + -1.583333334) = 2.256944447

Calculate the square root of the right side: 1.502313032

Break this problem into two subproblems by setting 
(x + -1.583333334) equal to 1.502313032 and -1.502313032.

Subproblem 1
x + -1.583333334 = 1.502313032

Simplifying
x + -1.583333334 = 1.502313032

Reorder the terms:
-1.583333334 + x = 1.502313032

Solving
-1.583333334 + x = 1.502313032

Solving for variable 'x'.

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

Add '1.583333334' to each side of the equation.
-1.583333334 + 1.583333334 + x = 1.502313032 + 1.583333334

Combine like terms: -1.583333334 + 1.583333334 = 0.000000000
0.000000000 + x = 1.502313032 + 1.583333334
x = 1.502313032 + 1.583333334

Combine like terms: 1.502313032 + 1.583333334 = 3.085646366
x = 3.085646366

Simplifying
x = 3.085646366

Subproblem 2
x + -1.583333334 = -1.502313032

Simplifying
x + -1.583333334 = -1.502313032

Reorder the terms:
-1.583333334 + x = -1.502313032

Solving
-1.583333334 + x = -1.502313032

Solving for variable 'x'.

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

Add '1.583333334' to each side of the equation.
-1.583333334 + 1.583333334 + x = -1.502313032 + 1.583333334

Combine like terms: -1.583333334 + 1.583333334 = 0.000000000
0.000000000 + x = -1.502313032 + 1.583333334
x = -1.502313032 + 1.583333334

Combine like terms: -1.502313032 + 1.583333334 = 0.081020302
x = 0.081020302

Simplifying
x = 0.081020302

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.085646366, 0.081020302}