3y^2+11y-134=0

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Solution for 3y^2+11y-134=0 equation: 


Simplifying
3y2 + 11y + -134 = 0

Reorder the terms:
-134 + 11y + 3y2 = 0

Solving
-134 + 11y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
-44.66666667 + 3.666666667y + y2 = 0

Move the constant term to the right:

Add '44.66666667' to each side of the equation.
-44.66666667 + 3.666666667y + 44.66666667 + y2 = 0 + 44.66666667

Reorder the terms:
-44.66666667 + 44.66666667 + 3.666666667y + y2 = 0 + 44.66666667

Combine like terms: -44.66666667 + 44.66666667 = 0.00000000
0.00000000 + 3.666666667y + y2 = 0 + 44.66666667
3.666666667y + y2 = 0 + 44.66666667

Combine like terms: 0 + 44.66666667 = 44.66666667
3.666666667y + y2 = 44.66666667

The y term is 3.666666667y.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667y + 3.361111114 + y2 = 44.66666667 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667y + y2 = 44.66666667 + 3.361111114

Combine like terms: 44.66666667 + 3.361111114 = 48.027777784
3.361111114 + 3.666666667y + y2 = 48.027777784

Factor a perfect square on the left side:
(y + 1.833333334)(y + 1.833333334) = 48.027777784

Calculate the square root of the right side: 6.930207629

Break this problem into two subproblems by setting 
(y + 1.833333334) equal to 6.930207629 and -6.930207629.


Subproblem 1
y + 1.833333334 = 6.930207629

Simplifying
y + 1.833333334 = 6.930207629

Reorder the terms:
1.833333334 + y = 6.930207629

Solving
1.833333334 + y = 6.930207629

Solving for variable 'y'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + y = 6.930207629 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + y = 6.930207629 + -1.833333334
y = 6.930207629 + -1.833333334

Combine like terms: 6.930207629 + -1.833333334 = 5.096874295
y = 5.096874295

Simplifying
y = 5.096874295


Subproblem 2
y + 1.833333334 = -6.930207629

Simplifying
y + 1.833333334 = -6.930207629

Reorder the terms:
1.833333334 + y = -6.930207629

Solving
1.833333334 + y = -6.930207629

Solving for variable 'y'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + y = -6.930207629 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + y = -6.930207629 + -1.833333334
y = -6.930207629 + -1.833333334

Combine like terms: -6.930207629 + -1.833333334 = -8.763540963
y = -8.763540963

Simplifying
y = -8.763540963


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.096874295, -8.763540963}

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