4u^2+8u-14=0

Solution for 4u^2+8u-14=0 equation:

Simplifying
4u2 + 8u + -14 = 0

Reorder the terms:
-14 + 8u + 4u2 = 0

Solving
-14 + 8u + 4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 4u + 2u2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + 4u + 2u2)' equal to zero and attempt to solve:

Simplifying
-7 + 4u + 2u2 = 0

Solving
-7 + 4u + 2u2 = 0

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

Divide each side by '2'.
-3.5 + 2u + u2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 2u + 3.5 + u2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 2u + u2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 2u + u2 = 0 + 3.5
2u + u2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
2u + u2 = 3.5

The u term is 2u.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2u + 1 + u2 = 3.5 + 1

Reorder the terms:
1 + 2u + u2 = 3.5 + 1

Combine like terms: 3.5 + 1 = 4.5
1 + 2u + u2 = 4.5

Factor a perfect square on the left side:
(u + 1)(u + 1) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(u + 1) equal to 2.121320344 and -2.121320344.

Subproblem 1
u + 1 = 2.121320344

Simplifying
u + 1 = 2.121320344

Reorder the terms:
1 + u = 2.121320344

Solving
1 + u = 2.121320344

Solving for variable 'u'.

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

Add '-1' to each side of the equation.
1 + -1 + u = 2.121320344 + -1

Combine like terms: 1 + -1 = 0
0 + u = 2.121320344 + -1
u = 2.121320344 + -1

Combine like terms: 2.121320344 + -1 = 1.121320344
u = 1.121320344

Simplifying
u = 1.121320344

Subproblem 2
u + 1 = -2.121320344

Simplifying
u + 1 = -2.121320344

Reorder the terms:
1 + u = -2.121320344

Solving
1 + u = -2.121320344

Solving for variable 'u'.

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

Add '-1' to each side of the equation.
1 + -1 + u = -2.121320344 + -1

Combine like terms: 1 + -1 = 0
0 + u = -2.121320344 + -1
u = -2.121320344 + -1

Combine like terms: -2.121320344 + -1 = -3.121320344
u = -3.121320344

Simplifying
u = -3.121320344

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.121320344, -3.121320344}
Solution
u = {1.121320344, -3.121320344}