6y^2-10y-5=0

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Solution for 6y^2-10y-5=0 equation: 


Simplifying
6y2 + -10y + -5 = 0

Reorder the terms:
-5 + -10y + 6y2 = 0

Solving
-5 + -10y + 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'.
-0.8333333333 + -1.666666667y + y2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -1.666666667y + 0.8333333333 + y2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -1.666666667y + y2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -1.666666667y + y2 = 0 + 0.8333333333
-1.666666667y + y2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-1.666666667y + y2 = 0.8333333333

The y term is -1.666666667y.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667y + 0.6944444447 + y2 = 0.8333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667y + y2 = 0.8333333333 + 0.6944444447

Combine like terms: 0.8333333333 + 0.6944444447 = 1.527777778
0.6944444447 + -1.666666667y + y2 = 1.527777778

Factor a perfect square on the left side:
(y + -0.8333333335)(y + -0.8333333335) = 1.527777778

Calculate the square root of the right side: 1.236033081

Break this problem into two subproblems by setting 
(y + -0.8333333335) equal to 1.236033081 and -1.236033081.


Subproblem 1
y + -0.8333333335 = 1.236033081

Simplifying
y + -0.8333333335 = 1.236033081

Reorder the terms:
-0.8333333335 + y = 1.236033081

Solving
-0.8333333335 + y = 1.236033081

Solving for variable 'y'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + y = 1.236033081 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + y = 1.236033081 + 0.8333333335
y = 1.236033081 + 0.8333333335

Combine like terms: 1.236033081 + 0.8333333335 = 2.0693664145
y = 2.0693664145

Simplifying
y = 2.0693664145


Subproblem 2
y + -0.8333333335 = -1.236033081

Simplifying
y + -0.8333333335 = -1.236033081

Reorder the terms:
-0.8333333335 + y = -1.236033081

Solving
-0.8333333335 + y = -1.236033081

Solving for variable 'y'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + y = -1.236033081 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + y = -1.236033081 + 0.8333333335
y = -1.236033081 + 0.8333333335

Combine like terms: -1.236033081 + 0.8333333335 = -0.4026997475
y = -0.4026997475

Simplifying
y = -0.4026997475


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.0693664145, -0.4026997475}

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