6u^2+19u+9=0

Solution for 6u^2+19u+9=0 equation:

Simplifying
6u2 + 19u + 9 = 0

Reorder the terms:
9 + 19u + 6u2 = 0

Solving
9 + 19u + 6u2 = 0

Solving for variable 'u'.

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

Divide each side by '6'.
1.5 + 3.166666667u + u2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 3.166666667u + -1.5 + u2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 3.166666667u + u2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 3.166666667u + u2 = 0 + -1.5
3.166666667u + u2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
3.166666667u + u2 = -1.5

The u term is 3.166666667u.  Take half its coefficient (1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
3.166666667u + 2.506944447 + u2 = -1.5 + 2.506944447

Reorder the terms:
2.506944447 + 3.166666667u + u2 = -1.5 + 2.506944447

Combine like terms: -1.5 + 2.506944447 = 1.006944447
2.506944447 + 3.166666667u + u2 = 1.006944447

Factor a perfect square on the left side:
(u + 1.583333334)(u + 1.583333334) = 1.006944447

Calculate the square root of the right side: 1.003466216

Break this problem into two subproblems by setting 
(u + 1.583333334) equal to 1.003466216 and -1.003466216.

Subproblem 1
u + 1.583333334 = 1.003466216

Simplifying
u + 1.583333334 = 1.003466216

Reorder the terms:
1.583333334 + u = 1.003466216

Solving
1.583333334 + u = 1.003466216

Solving for variable 'u'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + u = 1.003466216 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + u = 1.003466216 + -1.583333334
u = 1.003466216 + -1.583333334

Combine like terms: 1.003466216 + -1.583333334 = -0.579867118
u = -0.579867118

Simplifying
u = -0.579867118

Subproblem 2
u + 1.583333334 = -1.003466216

Simplifying
u + 1.583333334 = -1.003466216

Reorder the terms:
1.583333334 + u = -1.003466216

Solving
1.583333334 + u = -1.003466216

Solving for variable 'u'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + u = -1.003466216 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + u = -1.003466216 + -1.583333334
u = -1.003466216 + -1.583333334

Combine like terms: -1.003466216 + -1.583333334 = -2.58679955
u = -2.58679955

Simplifying
u = -2.58679955

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-0.579867118, -2.58679955}