-6y^2+7y+2=0

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Solution for -6y^2+7y+2=0 equation: 


Simplifying
-6y2 + 7y + 2 = 0

Reorder the terms:
2 + 7y + -6y2 = 0

Solving
2 + 7y + -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'.
-0.3333333333 + -1.166666667y + y2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -1.166666667y + 0.3333333333 + y2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -1.166666667y + y2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -1.166666667y + y2 = 0 + 0.3333333333
-1.166666667y + y2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-1.166666667y + y2 = 0.3333333333

The y term is -1.166666667y.  Take half its coefficient (-0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
-1.166666667y + 0.3402777780 + y2 = 0.3333333333 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667y + y2 = 0.3333333333 + 0.3402777780

Combine like terms: 0.3333333333 + 0.3402777780 = 0.6736111113
0.3402777780 + -1.166666667y + y2 = 0.6736111113

Factor a perfect square on the left side:
(y + -0.5833333335)(y + -0.5833333335) = 0.6736111113

Calculate the square root of the right side: 0.82073815

Break this problem into two subproblems by setting 
(y + -0.5833333335) equal to 0.82073815 and -0.82073815.


Subproblem 1
y + -0.5833333335 = 0.82073815

Simplifying
y + -0.5833333335 = 0.82073815

Reorder the terms:
-0.5833333335 + y = 0.82073815

Solving
-0.5833333335 + y = 0.82073815

Solving for variable 'y'.

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

Add '0.5833333335' to each side of the equation.
-0.5833333335 + 0.5833333335 + y = 0.82073815 + 0.5833333335

Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000
0.0000000000 + y = 0.82073815 + 0.5833333335
y = 0.82073815 + 0.5833333335

Combine like terms: 0.82073815 + 0.5833333335 = 1.4040714835
y = 1.4040714835

Simplifying
y = 1.4040714835


Subproblem 2
y + -0.5833333335 = -0.82073815

Simplifying
y + -0.5833333335 = -0.82073815

Reorder the terms:
-0.5833333335 + y = -0.82073815

Solving
-0.5833333335 + y = -0.82073815

Solving for variable 'y'.

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

Add '0.5833333335' to each side of the equation.
-0.5833333335 + 0.5833333335 + y = -0.82073815 + 0.5833333335

Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000
0.0000000000 + y = -0.82073815 + 0.5833333335
y = -0.82073815 + 0.5833333335

Combine like terms: -0.82073815 + 0.5833333335 = -0.2374048165
y = -0.2374048165

Simplifying
y = -0.2374048165


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.4040714835, -0.2374048165}

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