120y^2-12y-5=0

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Solution for 120y^2-12y-5=0 equation: 


Simplifying
120y2 + -12y + -5 = 0

Reorder the terms:
-5 + -12y + 120y2 = 0

Solving
-5 + -12y + 120y2 = 0

Solving for variable 'y'.

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

Divide each side by '120'.
-0.04166666667 + -0.1y + y2 = 0

Move the constant term to the right:

Add '0.04166666667' to each side of the equation.
-0.04166666667 + -0.1y + 0.04166666667 + y2 = 0 + 0.04166666667

Reorder the terms:
-0.04166666667 + 0.04166666667 + -0.1y + y2 = 0 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + -0.1y + y2 = 0 + 0.04166666667
-0.1y + y2 = 0 + 0.04166666667

Combine like terms: 0 + 0.04166666667 = 0.04166666667
-0.1y + y2 = 0.04166666667

The y term is -0.1y.  Take half its coefficient (-0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
-0.1y + 0.0025 + y2 = 0.04166666667 + 0.0025

Reorder the terms:
0.0025 + -0.1y + y2 = 0.04166666667 + 0.0025

Combine like terms: 0.04166666667 + 0.0025 = 0.04416666667
0.0025 + -0.1y + y2 = 0.04416666667

Factor a perfect square on the left side:
(y + -0.05)(y + -0.05) = 0.04416666667

Calculate the square root of the right side: 0.21015867

Break this problem into two subproblems by setting 
(y + -0.05) equal to 0.21015867 and -0.21015867.


Subproblem 1
y + -0.05 = 0.21015867

Simplifying
y + -0.05 = 0.21015867

Reorder the terms:
-0.05 + y = 0.21015867

Solving
-0.05 + y = 0.21015867

Solving for variable 'y'.

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

Add '0.05' to each side of the equation.
-0.05 + 0.05 + y = 0.21015867 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + y = 0.21015867 + 0.05
y = 0.21015867 + 0.05

Combine like terms: 0.21015867 + 0.05 = 0.26015867
y = 0.26015867

Simplifying
y = 0.26015867


Subproblem 2
y + -0.05 = -0.21015867

Simplifying
y + -0.05 = -0.21015867

Reorder the terms:
-0.05 + y = -0.21015867

Solving
-0.05 + y = -0.21015867

Solving for variable 'y'.

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

Add '0.05' to each side of the equation.
-0.05 + 0.05 + y = -0.21015867 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + y = -0.21015867 + 0.05
y = -0.21015867 + 0.05

Combine like terms: -0.21015867 + 0.05 = -0.16015867
y = -0.16015867

Simplifying
y = -0.16015867


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.26015867, -0.16015867}

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