39x^2-38x+12=21x^2+19x+19

Solution for 39x^2-38x+12=21x^2+19x+19 equation:

Simplifying
39x2 + -38x + 12 = 21x2 + 19x + 19

Reorder the terms:
12 + -38x + 39x2 = 21x2 + 19x + 19

Reorder the terms:
12 + -38x + 39x2 = 19 + 19x + 21x2

Solving
12 + -38x + 39x2 = 19 + 19x + 21x2

Solving for variable 'x'.

Reorder the terms:
12 + -19 + -38x + -19x + 39x2 + -21x2 = 19 + 19x + 21x2 + -19 + -19x + -21x2

Combine like terms: 12 + -19 = -7
-7 + -38x + -19x + 39x2 + -21x2 = 19 + 19x + 21x2 + -19 + -19x + -21x2

Combine like terms: -38x + -19x = -57x
-7 + -57x + 39x2 + -21x2 = 19 + 19x + 21x2 + -19 + -19x + -21x2

Combine like terms: 39x2 + -21x2 = 18x2
-7 + -57x + 18x2 = 19 + 19x + 21x2 + -19 + -19x + -21x2

Reorder the terms:
-7 + -57x + 18x2 = 19 + -19 + 19x + -19x + 21x2 + -21x2

Combine like terms: 19 + -19 = 0
-7 + -57x + 18x2 = 0 + 19x + -19x + 21x2 + -21x2
-7 + -57x + 18x2 = 19x + -19x + 21x2 + -21x2

Combine like terms: 19x + -19x = 0
-7 + -57x + 18x2 = 0 + 21x2 + -21x2
-7 + -57x + 18x2 = 21x2 + -21x2

Combine like terms: 21x2 + -21x2 = 0
-7 + -57x + 18x2 = 0

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

Divide each side by '18'.
-0.3888888889 + -3.166666667x + x2 = 0

Move the constant term to the right:

Add '0.3888888889' to each side of the equation.
-0.3888888889 + -3.166666667x + 0.3888888889 + x2 = 0 + 0.3888888889

Reorder the terms:
-0.3888888889 + 0.3888888889 + -3.166666667x + x2 = 0 + 0.3888888889

Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000
0.0000000000 + -3.166666667x + x2 = 0 + 0.3888888889
-3.166666667x + x2 = 0 + 0.3888888889

Combine like terms: 0 + 0.3888888889 = 0.3888888889
-3.166666667x + x2 = 0.3888888889

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 = 0.3888888889 + 2.506944447

Reorder the terms:
2.506944447 + -3.166666667x + x2 = 0.3888888889 + 2.506944447

Combine like terms: 0.3888888889 + 2.506944447 = 2.8958333359
2.506944447 + -3.166666667x + x2 = 2.8958333359

Factor a perfect square on the left side:
(x + -1.583333334)(x + -1.583333334) = 2.8958333359

Calculate the square root of the right side: 1.701714822

Break this problem into two subproblems by setting 
(x + -1.583333334) equal to 1.701714822 and -1.701714822.

Subproblem 1
x + -1.583333334 = 1.701714822

Simplifying
x + -1.583333334 = 1.701714822

Reorder the terms:
-1.583333334 + x = 1.701714822

Solving
-1.583333334 + x = 1.701714822

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 = 1.701714822 + 1.583333334

Combine like terms: -1.583333334 + 1.583333334 = 0.000000000
0.000000000 + x = 1.701714822 + 1.583333334
x = 1.701714822 + 1.583333334

Combine like terms: 1.701714822 + 1.583333334 = 3.285048156
x = 3.285048156

Simplifying
x = 3.285048156

Subproblem 2
x + -1.583333334 = -1.701714822

Simplifying
x + -1.583333334 = -1.701714822

Reorder the terms:
-1.583333334 + x = -1.701714822

Solving
-1.583333334 + x = -1.701714822

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 = -1.701714822 + 1.583333334

Combine like terms: -1.583333334 + 1.583333334 = 0.000000000
0.000000000 + x = -1.701714822 + 1.583333334
x = -1.701714822 + 1.583333334

Combine like terms: -1.701714822 + 1.583333334 = -0.118381488
x = -0.118381488

Simplifying
x = -0.118381488

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.285048156, -0.118381488}