38x^2+6x-10=0

Solution for 38x^2+6x-10=0 equation:

Simplifying
38x2 + 6x + -10 = 0

Reorder the terms:
-10 + 6x + 38x2 = 0

Solving
-10 + 6x + 38x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 3x + 19x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 3x + 19x2)' equal to zero and attempt to solve:

Simplifying
-5 + 3x + 19x2 = 0

Solving
-5 + 3x + 19x2 = 0

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

Divide each side by '19'.
-0.2631578947 + 0.1578947368x + x2 = 0

Move the constant term to the right:

Add '0.2631578947' to each side of the equation.
-0.2631578947 + 0.1578947368x + 0.2631578947 + x2 = 0 + 0.2631578947

Reorder the terms:
-0.2631578947 + 0.2631578947 + 0.1578947368x + x2 = 0 + 0.2631578947

Combine like terms: -0.2631578947 + 0.2631578947 = 0.0000000000
0.0000000000 + 0.1578947368x + x2 = 0 + 0.2631578947
0.1578947368x + x2 = 0 + 0.2631578947

Combine like terms: 0 + 0.2631578947 = 0.2631578947
0.1578947368x + x2 = 0.2631578947

The x term is 0.1578947368x.  Take half its coefficient (0.0789473684).
Square it (0.006232686977) and add it to both sides.

Add '0.006232686977' to each side of the equation.
0.1578947368x + 0.006232686977 + x2 = 0.2631578947 + 0.006232686977

Reorder the terms:
0.006232686977 + 0.1578947368x + x2 = 0.2631578947 + 0.006232686977

Combine like terms: 0.2631578947 + 0.006232686977 = 0.269390581677
0.006232686977 + 0.1578947368x + x2 = 0.269390581677

Factor a perfect square on the left side:
(x + 0.0789473684)(x + 0.0789473684) = 0.269390581677

Calculate the square root of the right side: 0.519028498

Break this problem into two subproblems by setting 
(x + 0.0789473684) equal to 0.519028498 and -0.519028498.

Subproblem 1
x + 0.0789473684 = 0.519028498

Simplifying
x + 0.0789473684 = 0.519028498

Reorder the terms:
0.0789473684 + x = 0.519028498

Solving
0.0789473684 + x = 0.519028498

Solving for variable 'x'.

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

Add '-0.0789473684' to each side of the equation.
0.0789473684 + -0.0789473684 + x = 0.519028498 + -0.0789473684

Combine like terms: 0.0789473684 + -0.0789473684 = 0.0000000000
0.0000000000 + x = 0.519028498 + -0.0789473684
x = 0.519028498 + -0.0789473684

Combine like terms: 0.519028498 + -0.0789473684 = 0.4400811296
x = 0.4400811296

Simplifying
x = 0.4400811296

Subproblem 2
x + 0.0789473684 = -0.519028498

Simplifying
x + 0.0789473684 = -0.519028498

Reorder the terms:
0.0789473684 + x = -0.519028498

Solving
0.0789473684 + x = -0.519028498

Solving for variable 'x'.

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

Add '-0.0789473684' to each side of the equation.
0.0789473684 + -0.0789473684 + x = -0.519028498 + -0.0789473684

Combine like terms: 0.0789473684 + -0.0789473684 = 0.0000000000
0.0000000000 + x = -0.519028498 + -0.0789473684
x = -0.519028498 + -0.0789473684

Combine like terms: -0.519028498 + -0.0789473684 = -0.5979758664
x = -0.5979758664

Simplifying
x = -0.5979758664

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4400811296, -0.5979758664}
Solution
x = {0.4400811296, -0.5979758664}