6y^2-y-4=0

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Solution for 6y^2-y-4=0 equation: 


Simplifying
6y2 + -1y + -4 = 0

Reorder the terms:
-4 + -1y + 6y2 = 0

Solving
-4 + -1y + 6y2 = 0

Solving for variable 'y'.

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

Divide each side by '6'.
-0.6666666667 + -0.1666666667y + y2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -0.1666666667y + 0.6666666667 + y2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -0.1666666667y + y2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -0.1666666667y + y2 = 0 + 0.6666666667
-0.1666666667y + y2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-0.1666666667y + y2 = 0.6666666667

The y term is -0.1666666667y.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667y + 0.006944444447 + y2 = 0.6666666667 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667y + y2 = 0.6666666667 + 0.006944444447

Combine like terms: 0.6666666667 + 0.006944444447 = 0.673611111147
0.006944444447 + -0.1666666667y + y2 = 0.673611111147

Factor a perfect square on the left side:
(y + -0.08333333335)(y + -0.08333333335) = 0.673611111147

Calculate the square root of the right side: 0.82073815

Break this problem into two subproblems by setting 
(y + -0.08333333335) equal to 0.82073815 and -0.82073815.


Subproblem 1
y + -0.08333333335 = 0.82073815

Simplifying
y + -0.08333333335 = 0.82073815

Reorder the terms:
-0.08333333335 + y = 0.82073815

Solving
-0.08333333335 + y = 0.82073815

Solving for variable 'y'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + y = 0.82073815 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + y = 0.82073815 + 0.08333333335
y = 0.82073815 + 0.08333333335

Combine like terms: 0.82073815 + 0.08333333335 = 0.90407148335
y = 0.90407148335

Simplifying
y = 0.90407148335


Subproblem 2
y + -0.08333333335 = -0.82073815

Simplifying
y + -0.08333333335 = -0.82073815

Reorder the terms:
-0.08333333335 + y = -0.82073815

Solving
-0.08333333335 + y = -0.82073815

Solving for variable 'y'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + y = -0.82073815 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + y = -0.82073815 + 0.08333333335
y = -0.82073815 + 0.08333333335

Combine like terms: -0.82073815 + 0.08333333335 = -0.73740481665
y = -0.73740481665

Simplifying
y = -0.73740481665


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.90407148335, -0.73740481665}

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