14x^2-92x-48=0

Solution for 14x^2-92x-48=0 equation:

Simplifying
14x2 + -92x + -48 = 0

Reorder the terms:
-48 + -92x + 14x2 = 0

Solving
-48 + -92x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -46x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-24 + -46x + 7x2)' equal to zero and attempt to solve:

Simplifying
-24 + -46x + 7x2 = 0

Solving
-24 + -46x + 7x2 = 0

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

Divide each side by '7'.
-3.428571429 + -6.571428571x + x2 = 0

Move the constant term to the right:

Add '3.428571429' to each side of the equation.
-3.428571429 + -6.571428571x + 3.428571429 + x2 = 0 + 3.428571429

Reorder the terms:
-3.428571429 + 3.428571429 + -6.571428571x + x2 = 0 + 3.428571429

Combine like terms: -3.428571429 + 3.428571429 = 0.000000000
0.000000000 + -6.571428571x + x2 = 0 + 3.428571429
-6.571428571x + x2 = 0 + 3.428571429

Combine like terms: 0 + 3.428571429 = 3.428571429
-6.571428571x + x2 = 3.428571429

The x term is -6.571428571x.  Take half its coefficient (-3.285714286).
Square it (10.79591837) and add it to both sides.

Add '10.79591837' to each side of the equation.
-6.571428571x + 10.79591837 + x2 = 3.428571429 + 10.79591837

Reorder the terms:
10.79591837 + -6.571428571x + x2 = 3.428571429 + 10.79591837

Combine like terms: 3.428571429 + 10.79591837 = 14.224489799
10.79591837 + -6.571428571x + x2 = 14.224489799

Factor a perfect square on the left side:
(x + -3.285714286)(x + -3.285714286) = 14.224489799

Calculate the square root of the right side: 3.771536795

Break this problem into two subproblems by setting 
(x + -3.285714286) equal to 3.771536795 and -3.771536795.

Subproblem 1
x + -3.285714286 = 3.771536795

Simplifying
x + -3.285714286 = 3.771536795

Reorder the terms:
-3.285714286 + x = 3.771536795

Solving
-3.285714286 + x = 3.771536795

Solving for variable 'x'.

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

Add '3.285714286' to each side of the equation.
-3.285714286 + 3.285714286 + x = 3.771536795 + 3.285714286

Combine like terms: -3.285714286 + 3.285714286 = 0.000000000
0.000000000 + x = 3.771536795 + 3.285714286
x = 3.771536795 + 3.285714286

Combine like terms: 3.771536795 + 3.285714286 = 7.057251081
x = 7.057251081

Simplifying
x = 7.057251081

Subproblem 2
x + -3.285714286 = -3.771536795

Simplifying
x + -3.285714286 = -3.771536795

Reorder the terms:
-3.285714286 + x = -3.771536795

Solving
-3.285714286 + x = -3.771536795

Solving for variable 'x'.

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

Add '3.285714286' to each side of the equation.
-3.285714286 + 3.285714286 + x = -3.771536795 + 3.285714286

Combine like terms: -3.285714286 + 3.285714286 = 0.000000000
0.000000000 + x = -3.771536795 + 3.285714286
x = -3.771536795 + 3.285714286

Combine like terms: -3.771536795 + 3.285714286 = -0.485822509
x = -0.485822509

Simplifying
x = -0.485822509

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.057251081, -0.485822509}
Solution
x = {7.057251081, -0.485822509}