6y^2-y-16=0

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Solution for 6y^2-y-16=0 equation: 


Simplifying
6y2 + -1y + -16 = 0

Reorder the terms:
-16 + -1y + 6y2 = 0

Solving
-16 + -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'.
-2.666666667 + -0.1666666667y + y2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -0.1666666667y + 2.666666667 + y2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -0.1666666667y + y2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -0.1666666667y + y2 = 0 + 2.666666667
-0.1666666667y + y2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-0.1666666667y + y2 = 2.666666667

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 = 2.666666667 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667y + y2 = 2.666666667 + 0.006944444447

Combine like terms: 2.666666667 + 0.006944444447 = 2.673611111447
0.006944444447 + -0.1666666667y + y2 = 2.673611111447

Factor a perfect square on the left side:
(y + -0.08333333335)(y + -0.08333333335) = 2.673611111447

Calculate the square root of the right side: 1.635118073

Break this problem into two subproblems by setting 
(y + -0.08333333335) equal to 1.635118073 and -1.635118073.


Subproblem 1
y + -0.08333333335 = 1.635118073

Simplifying
y + -0.08333333335 = 1.635118073

Reorder the terms:
-0.08333333335 + y = 1.635118073

Solving
-0.08333333335 + y = 1.635118073

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 = 1.635118073 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + y = 1.635118073 + 0.08333333335
y = 1.635118073 + 0.08333333335

Combine like terms: 1.635118073 + 0.08333333335 = 1.71845140635
y = 1.71845140635

Simplifying
y = 1.71845140635


Subproblem 2
y + -0.08333333335 = -1.635118073

Simplifying
y + -0.08333333335 = -1.635118073

Reorder the terms:
-0.08333333335 + y = -1.635118073

Solving
-0.08333333335 + y = -1.635118073

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 = -1.635118073 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + y = -1.635118073 + 0.08333333335
y = -1.635118073 + 0.08333333335

Combine like terms: -1.635118073 + 0.08333333335 = -1.55178473965
y = -1.55178473965

Simplifying
y = -1.55178473965


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.71845140635, -1.55178473965}

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