-14x^2+6x+32=0

Solution for -14x^2+6x+32=0 equation:

Simplifying
-14x2 + 6x + 32 = 0

Reorder the terms:
32 + 6x + -14x2 = 0

Solving
32 + 6x + -14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 3x + -7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(16 + 3x + -7x2)' equal to zero and attempt to solve:

Simplifying
16 + 3x + -7x2 = 0

Solving
16 + 3x + -7x2 = 0

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

Divide each side by '-7'.
-2.285714286 + -0.4285714286x + x2 = 0

Move the constant term to the right:

Add '2.285714286' to each side of the equation.
-2.285714286 + -0.4285714286x + 2.285714286 + x2 = 0 + 2.285714286

Reorder the terms:
-2.285714286 + 2.285714286 + -0.4285714286x + x2 = 0 + 2.285714286

Combine like terms: -2.285714286 + 2.285714286 = 0.000000000
0.000000000 + -0.4285714286x + x2 = 0 + 2.285714286
-0.4285714286x + x2 = 0 + 2.285714286

Combine like terms: 0 + 2.285714286 = 2.285714286
-0.4285714286x + x2 = 2.285714286

The x term is -0.4285714286x.  Take half its coefficient (-0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
-0.4285714286x + 0.04591836735 + x2 = 2.285714286 + 0.04591836735

Reorder the terms:
0.04591836735 + -0.4285714286x + x2 = 2.285714286 + 0.04591836735

Combine like terms: 2.285714286 + 0.04591836735 = 2.33163265335
0.04591836735 + -0.4285714286x + x2 = 2.33163265335

Factor a perfect square on the left side:
(x + -0.2142857143)(x + -0.2142857143) = 2.33163265335

Calculate the square root of the right side: 1.526968452

Break this problem into two subproblems by setting 
(x + -0.2142857143) equal to 1.526968452 and -1.526968452.

Subproblem 1
x + -0.2142857143 = 1.526968452

Simplifying
x + -0.2142857143 = 1.526968452

Reorder the terms:
-0.2142857143 + x = 1.526968452

Solving
-0.2142857143 + x = 1.526968452

Solving for variable 'x'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + x = 1.526968452 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + x = 1.526968452 + 0.2142857143
x = 1.526968452 + 0.2142857143

Combine like terms: 1.526968452 + 0.2142857143 = 1.7412541663
x = 1.7412541663

Simplifying
x = 1.7412541663

Subproblem 2
x + -0.2142857143 = -1.526968452

Simplifying
x + -0.2142857143 = -1.526968452

Reorder the terms:
-0.2142857143 + x = -1.526968452

Solving
-0.2142857143 + x = -1.526968452

Solving for variable 'x'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + x = -1.526968452 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + x = -1.526968452 + 0.2142857143
x = -1.526968452 + 0.2142857143

Combine like terms: -1.526968452 + 0.2142857143 = -1.3126827377
x = -1.3126827377

Simplifying
x = -1.3126827377

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.7412541663, -1.3126827377}
Solution
x = {1.7412541663, -1.3126827377}