-6y^2-10y+73=0

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Solution for -6y^2-10y+73=0 equation: 


Simplifying
-6y2 + -10y + 73 = 0

Reorder the terms:
73 + -10y + -6y2 = 0

Solving
73 + -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'.
-12.16666667 + 1.666666667y + y2 = 0

Move the constant term to the right:

Add '12.16666667' to each side of the equation.
-12.16666667 + 1.666666667y + 12.16666667 + y2 = 0 + 12.16666667

Reorder the terms:
-12.16666667 + 12.16666667 + 1.666666667y + y2 = 0 + 12.16666667

Combine like terms: -12.16666667 + 12.16666667 = 0.00000000
0.00000000 + 1.666666667y + y2 = 0 + 12.16666667
1.666666667y + y2 = 0 + 12.16666667

Combine like terms: 0 + 12.16666667 = 12.16666667
1.666666667y + y2 = 12.16666667

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 = 12.16666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667y + y2 = 12.16666667 + 0.6944444447

Combine like terms: 12.16666667 + 0.6944444447 = 12.8611111147
0.6944444447 + 1.666666667y + y2 = 12.8611111147

Factor a perfect square on the left side:
(y + 0.8333333335)(y + 0.8333333335) = 12.8611111147

Calculate the square root of the right side: 3.586239132

Break this problem into two subproblems by setting 
(y + 0.8333333335) equal to 3.586239132 and -3.586239132.


Subproblem 1
y + 0.8333333335 = 3.586239132

Simplifying
y + 0.8333333335 = 3.586239132

Reorder the terms:
0.8333333335 + y = 3.586239132

Solving
0.8333333335 + y = 3.586239132

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 = 3.586239132 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + y = 3.586239132 + -0.8333333335
y = 3.586239132 + -0.8333333335

Combine like terms: 3.586239132 + -0.8333333335 = 2.7529057985
y = 2.7529057985

Simplifying
y = 2.7529057985


Subproblem 2
y + 0.8333333335 = -3.586239132

Simplifying
y + 0.8333333335 = -3.586239132

Reorder the terms:
0.8333333335 + y = -3.586239132

Solving
0.8333333335 + y = -3.586239132

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 = -3.586239132 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + y = -3.586239132 + -0.8333333335
y = -3.586239132 + -0.8333333335

Combine like terms: -3.586239132 + -0.8333333335 = -4.4195724655
y = -4.4195724655

Simplifying
y = -4.4195724655


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.7529057985, -4.4195724655}

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