14u^2-13u-6=0

Solution for 14u^2-13u-6=0 equation:

Simplifying
14u2 + -13u + -6 = 0

Reorder the terms:
-6 + -13u + 14u2 = 0

Solving
-6 + -13u + 14u2 = 0

Solving for variable 'u'.

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

Divide each side by '14'.
-0.4285714286 + -0.9285714286u + u2 = 0

Move the constant term to the right:

Add '0.4285714286' to each side of the equation.
-0.4285714286 + -0.9285714286u + 0.4285714286 + u2 = 0 + 0.4285714286

Reorder the terms:
-0.4285714286 + 0.4285714286 + -0.9285714286u + u2 = 0 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + -0.9285714286u + u2 = 0 + 0.4285714286
-0.9285714286u + u2 = 0 + 0.4285714286

Combine like terms: 0 + 0.4285714286 = 0.4285714286
-0.9285714286u + u2 = 0.4285714286

The u term is -0.9285714286u.  Take half its coefficient (-0.4642857143).
Square it (0.2155612245) and add it to both sides.

Add '0.2155612245' to each side of the equation.
-0.9285714286u + 0.2155612245 + u2 = 0.4285714286 + 0.2155612245

Reorder the terms:
0.2155612245 + -0.9285714286u + u2 = 0.4285714286 + 0.2155612245

Combine like terms: 0.4285714286 + 0.2155612245 = 0.6441326531
0.2155612245 + -0.9285714286u + u2 = 0.6441326531

Factor a perfect square on the left side:
(u + -0.4642857143)(u + -0.4642857143) = 0.6441326531

Calculate the square root of the right side: 0.802578752

Break this problem into two subproblems by setting 
(u + -0.4642857143) equal to 0.802578752 and -0.802578752.

Subproblem 1
u + -0.4642857143 = 0.802578752

Simplifying
u + -0.4642857143 = 0.802578752

Reorder the terms:
-0.4642857143 + u = 0.802578752

Solving
-0.4642857143 + u = 0.802578752

Solving for variable 'u'.

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

Add '0.4642857143' to each side of the equation.
-0.4642857143 + 0.4642857143 + u = 0.802578752 + 0.4642857143

Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000
0.0000000000 + u = 0.802578752 + 0.4642857143
u = 0.802578752 + 0.4642857143

Combine like terms: 0.802578752 + 0.4642857143 = 1.2668644663
u = 1.2668644663

Simplifying
u = 1.2668644663

Subproblem 2
u + -0.4642857143 = -0.802578752

Simplifying
u + -0.4642857143 = -0.802578752

Reorder the terms:
-0.4642857143 + u = -0.802578752

Solving
-0.4642857143 + u = -0.802578752

Solving for variable 'u'.

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

Add '0.4642857143' to each side of the equation.
-0.4642857143 + 0.4642857143 + u = -0.802578752 + 0.4642857143

Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000
0.0000000000 + u = -0.802578752 + 0.4642857143
u = -0.802578752 + 0.4642857143

Combine like terms: -0.802578752 + 0.4642857143 = -0.3382930377
u = -0.3382930377

Simplifying
u = -0.3382930377

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.2668644663, -0.3382930377}