(8x^2-2x-38)+(6x^2+4)=0

Solution for (8x^2-2x-38)+(6x^2+4)=0 equation:

Simplifying
(8x2 + -2x + -38) + (6x2 + 4) = 0

Reorder the terms:
(-38 + -2x + 8x2) + (6x2 + 4) = 0

Remove parenthesis around (-38 + -2x + 8x2)
-38 + -2x + 8x2 + (6x2 + 4) = 0

Reorder the terms:
-38 + -2x + 8x2 + (4 + 6x2) = 0

Remove parenthesis around (4 + 6x2)
-38 + -2x + 8x2 + 4 + 6x2 = 0

Reorder the terms:
-38 + 4 + -2x + 8x2 + 6x2 = 0

Combine like terms: -38 + 4 = -34
-34 + -2x + 8x2 + 6x2 = 0

Combine like terms: 8x2 + 6x2 = 14x2
-34 + -2x + 14x2 = 0

Solving
-34 + -2x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + -1x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + -1x + 7x2)' equal to zero and attempt to solve:

Simplifying
-17 + -1x + 7x2 = 0

Solving
-17 + -1x + 7x2 = 0

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

Divide each side by '7'.
-2.428571429 + -0.1428571429x + x2 = 0

Move the constant term to the right:

Add '2.428571429' to each side of the equation.
-2.428571429 + -0.1428571429x + 2.428571429 + x2 = 0 + 2.428571429

Reorder the terms:
-2.428571429 + 2.428571429 + -0.1428571429x + x2 = 0 + 2.428571429

Combine like terms: -2.428571429 + 2.428571429 = 0.000000000
0.000000000 + -0.1428571429x + x2 = 0 + 2.428571429
-0.1428571429x + x2 = 0 + 2.428571429

Combine like terms: 0 + 2.428571429 = 2.428571429
-0.1428571429x + x2 = 2.428571429

The x term is -0.1428571429x.  Take half its coefficient (-0.07142857145).
Square it (0.005102040819) and add it to both sides.

Add '0.005102040819' to each side of the equation.
-0.1428571429x + 0.005102040819 + x2 = 2.428571429 + 0.005102040819

Reorder the terms:
0.005102040819 + -0.1428571429x + x2 = 2.428571429 + 0.005102040819

Combine like terms: 2.428571429 + 0.005102040819 = 2.433673469819
0.005102040819 + -0.1428571429x + x2 = 2.433673469819

Factor a perfect square on the left side:
(x + -0.07142857145)(x + -0.07142857145) = 2.433673469819

Calculate the square root of the right side: 1.560023548

Break this problem into two subproblems by setting 
(x + -0.07142857145) equal to 1.560023548 and -1.560023548.

Subproblem 1
x + -0.07142857145 = 1.560023548

Simplifying
x + -0.07142857145 = 1.560023548

Reorder the terms:
-0.07142857145 + x = 1.560023548

Solving
-0.07142857145 + x = 1.560023548

Solving for variable 'x'.

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

Add '0.07142857145' to each side of the equation.
-0.07142857145 + 0.07142857145 + x = 1.560023548 + 0.07142857145

Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000
0.00000000000 + x = 1.560023548 + 0.07142857145
x = 1.560023548 + 0.07142857145

Combine like terms: 1.560023548 + 0.07142857145 = 1.63145211945
x = 1.63145211945

Simplifying
x = 1.63145211945

Subproblem 2
x + -0.07142857145 = -1.560023548

Simplifying
x + -0.07142857145 = -1.560023548

Reorder the terms:
-0.07142857145 + x = -1.560023548

Solving
-0.07142857145 + x = -1.560023548

Solving for variable 'x'.

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

Add '0.07142857145' to each side of the equation.
-0.07142857145 + 0.07142857145 + x = -1.560023548 + 0.07142857145

Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000
0.00000000000 + x = -1.560023548 + 0.07142857145
x = -1.560023548 + 0.07142857145

Combine like terms: -1.560023548 + 0.07142857145 = -1.48859497655
x = -1.48859497655

Simplifying
x = -1.48859497655

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.63145211945, -1.48859497655}
Solution
x = {1.63145211945, -1.48859497655}