3y^2-8y-49=0

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Solution for 3y^2-8y-49=0 equation: 


Simplifying
3y2 + -8y + -49 = 0

Reorder the terms:
-49 + -8y + 3y2 = 0

Solving
-49 + -8y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
-16.33333333 + -2.666666667y + y2 = 0

Move the constant term to the right:

Add '16.33333333' to each side of the equation.
-16.33333333 + -2.666666667y + 16.33333333 + y2 = 0 + 16.33333333

Reorder the terms:
-16.33333333 + 16.33333333 + -2.666666667y + y2 = 0 + 16.33333333

Combine like terms: -16.33333333 + 16.33333333 = 0.00000000
0.00000000 + -2.666666667y + y2 = 0 + 16.33333333
-2.666666667y + y2 = 0 + 16.33333333

Combine like terms: 0 + 16.33333333 = 16.33333333
-2.666666667y + y2 = 16.33333333

The y term is -2.666666667y.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667y + 1.777777780 + y2 = 16.33333333 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667y + y2 = 16.33333333 + 1.777777780

Combine like terms: 16.33333333 + 1.777777780 = 18.11111111
1.777777780 + -2.666666667y + y2 = 18.11111111

Factor a perfect square on the left side:
(y + -1.333333334)(y + -1.333333334) = 18.11111111

Calculate the square root of the right side: 4.255715111

Break this problem into two subproblems by setting 
(y + -1.333333334) equal to 4.255715111 and -4.255715111.


Subproblem 1
y + -1.333333334 = 4.255715111

Simplifying
y + -1.333333334 = 4.255715111

Reorder the terms:
-1.333333334 + y = 4.255715111

Solving
-1.333333334 + y = 4.255715111

Solving for variable 'y'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + y = 4.255715111 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + y = 4.255715111 + 1.333333334
y = 4.255715111 + 1.333333334

Combine like terms: 4.255715111 + 1.333333334 = 5.589048445
y = 5.589048445

Simplifying
y = 5.589048445


Subproblem 2
y + -1.333333334 = -4.255715111

Simplifying
y + -1.333333334 = -4.255715111

Reorder the terms:
-1.333333334 + y = -4.255715111

Solving
-1.333333334 + y = -4.255715111

Solving for variable 'y'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + y = -4.255715111 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + y = -4.255715111 + 1.333333334
y = -4.255715111 + 1.333333334

Combine like terms: -4.255715111 + 1.333333334 = -2.922381777
y = -2.922381777

Simplifying
y = -2.922381777


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.589048445, -2.922381777}

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