9u^2-29u-54=0

Solution for 9u^2-29u-54=0 equation:

Simplifying
9u2 + -29u + -54 = 0

Reorder the terms:
-54 + -29u + 9u2 = 0

Solving
-54 + -29u + 9u2 = 0

Solving for variable 'u'.

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

Divide each side by '9'.
-6 + -3.222222222u + u2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -3.222222222u + 6 + u2 = 0 + 6

Reorder the terms:
-6 + 6 + -3.222222222u + u2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -3.222222222u + u2 = 0 + 6
-3.222222222u + u2 = 0 + 6

Combine like terms: 0 + 6 = 6
-3.222222222u + u2 = 6

The u term is -3.222222222u.  Take half its coefficient (-1.611111111).
Square it (2.595679012) and add it to both sides.

Add '2.595679012' to each side of the equation.
-3.222222222u + 2.595679012 + u2 = 6 + 2.595679012

Reorder the terms:
2.595679012 + -3.222222222u + u2 = 6 + 2.595679012

Combine like terms: 6 + 2.595679012 = 8.595679012
2.595679012 + -3.222222222u + u2 = 8.595679012

Factor a perfect square on the left side:
(u + -1.611111111)(u + -1.611111111) = 8.595679012

Calculate the square root of the right side: 2.931838845

Break this problem into two subproblems by setting 
(u + -1.611111111) equal to 2.931838845 and -2.931838845.

Subproblem 1
u + -1.611111111 = 2.931838845

Simplifying
u + -1.611111111 = 2.931838845

Reorder the terms:
-1.611111111 + u = 2.931838845

Solving
-1.611111111 + u = 2.931838845

Solving for variable 'u'.

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

Add '1.611111111' to each side of the equation.
-1.611111111 + 1.611111111 + u = 2.931838845 + 1.611111111

Combine like terms: -1.611111111 + 1.611111111 = 0.000000000
0.000000000 + u = 2.931838845 + 1.611111111
u = 2.931838845 + 1.611111111

Combine like terms: 2.931838845 + 1.611111111 = 4.542949956
u = 4.542949956

Simplifying
u = 4.542949956

Subproblem 2
u + -1.611111111 = -2.931838845

Simplifying
u + -1.611111111 = -2.931838845

Reorder the terms:
-1.611111111 + u = -2.931838845

Solving
-1.611111111 + u = -2.931838845

Solving for variable 'u'.

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

Add '1.611111111' to each side of the equation.
-1.611111111 + 1.611111111 + u = -2.931838845 + 1.611111111

Combine like terms: -1.611111111 + 1.611111111 = 0.000000000
0.000000000 + u = -2.931838845 + 1.611111111
u = -2.931838845 + 1.611111111

Combine like terms: -2.931838845 + 1.611111111 = -1.320727734
u = -1.320727734

Simplifying
u = -1.320727734

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {4.542949956, -1.320727734}