8u^2+16u-19=0

Solution for 8u^2+16u-19=0 equation:

Simplifying
8u2 + 16u + -19 = 0

Reorder the terms:
-19 + 16u + 8u2 = 0

Solving
-19 + 16u + 8u2 = 0

Solving for variable 'u'.

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

Divide each side by '8'.
-2.375 + 2u + u2 = 0

Move the constant term to the right:

Add '2.375' to each side of the equation.
-2.375 + 2u + 2.375 + u2 = 0 + 2.375

Reorder the terms:
-2.375 + 2.375 + 2u + u2 = 0 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + 2u + u2 = 0 + 2.375
2u + u2 = 0 + 2.375

Combine like terms: 0 + 2.375 = 2.375
2u + u2 = 2.375

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 = 2.375 + 1

Reorder the terms:
1 + 2u + u2 = 2.375 + 1

Combine like terms: 2.375 + 1 = 3.375
1 + 2u + u2 = 3.375

Factor a perfect square on the left side:
(u + 1)(u + 1) = 3.375

Calculate the square root of the right side: 1.837117307

Break this problem into two subproblems by setting 
(u + 1) equal to 1.837117307 and -1.837117307.

Subproblem 1
u + 1 = 1.837117307

Simplifying
u + 1 = 1.837117307

Reorder the terms:
1 + u = 1.837117307

Solving
1 + u = 1.837117307

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 = 1.837117307 + -1

Combine like terms: 1 + -1 = 0
0 + u = 1.837117307 + -1
u = 1.837117307 + -1

Combine like terms: 1.837117307 + -1 = 0.837117307
u = 0.837117307

Simplifying
u = 0.837117307

Subproblem 2
u + 1 = -1.837117307

Simplifying
u + 1 = -1.837117307

Reorder the terms:
1 + u = -1.837117307

Solving
1 + u = -1.837117307

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 = -1.837117307 + -1

Combine like terms: 1 + -1 = 0
0 + u = -1.837117307 + -1
u = -1.837117307 + -1

Combine like terms: -1.837117307 + -1 = -2.837117307
u = -2.837117307

Simplifying
u = -2.837117307

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.837117307, -2.837117307}