6u^2-11u-20=

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Solution for 6u^2-11u-20= equation: 


Simplifying
6u2 + -11u + -20 = 0

Reorder the terms:
-20 + -11u + 6u2 = 0

Solving
-20 + -11u + 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'.
-3.333333333 + -1.833333333u + u2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -1.833333333u + 3.333333333 + u2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -1.833333333u + u2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -1.833333333u + u2 = 0 + 3.333333333
-1.833333333u + u2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-1.833333333u + u2 = 3.333333333

The u term is -1.833333333u.  Take half its coefficient (-0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
-1.833333333u + 0.8402777775 + u2 = 3.333333333 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333u + u2 = 3.333333333 + 0.8402777775

Combine like terms: 3.333333333 + 0.8402777775 = 4.1736111105
0.8402777775 + -1.833333333u + u2 = 4.1736111105

Factor a perfect square on the left side:
(u + -0.9166666665)(u + -0.9166666665) = 4.1736111105

Calculate the square root of the right side: 2.042941779

Break this problem into two subproblems by setting 
(u + -0.9166666665) equal to 2.042941779 and -2.042941779.


Subproblem 1
u + -0.9166666665 = 2.042941779

Simplifying
u + -0.9166666665 = 2.042941779

Reorder the terms:
-0.9166666665 + u = 2.042941779

Solving
-0.9166666665 + u = 2.042941779

Solving for variable 'u'.

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

Add '0.9166666665' to each side of the equation.
-0.9166666665 + 0.9166666665 + u = 2.042941779 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + u = 2.042941779 + 0.9166666665
u = 2.042941779 + 0.9166666665

Combine like terms: 2.042941779 + 0.9166666665 = 2.9596084455
u = 2.9596084455

Simplifying
u = 2.9596084455


Subproblem 2
u + -0.9166666665 = -2.042941779

Simplifying
u + -0.9166666665 = -2.042941779

Reorder the terms:
-0.9166666665 + u = -2.042941779

Solving
-0.9166666665 + u = -2.042941779

Solving for variable 'u'.

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

Add '0.9166666665' to each side of the equation.
-0.9166666665 + 0.9166666665 + u = -2.042941779 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + u = -2.042941779 + 0.9166666665
u = -2.042941779 + 0.9166666665

Combine like terms: -2.042941779 + 0.9166666665 = -1.1262751125
u = -1.1262751125

Simplifying
u = -1.1262751125


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {2.9596084455, -1.1262751125}

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