3y^2-17y-4=0

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Solution for 3y^2-17y-4=0 equation: 


Simplifying
3y2 + -17y + -4 = 0

Reorder the terms:
-4 + -17y + 3y2 = 0

Solving
-4 + -17y + 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'.
-1.333333333 + -5.666666667y + y2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -5.666666667y + 1.333333333 + y2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -5.666666667y + y2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -5.666666667y + y2 = 0 + 1.333333333
-5.666666667y + y2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-5.666666667y + y2 = 1.333333333

The y term is -5.666666667y.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667y + 8.027777782 + y2 = 1.333333333 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667y + y2 = 1.333333333 + 8.027777782

Combine like terms: 1.333333333 + 8.027777782 = 9.361111115
8.027777782 + -5.666666667y + y2 = 9.361111115

Factor a perfect square on the left side:
(y + -2.833333334)(y + -2.833333334) = 9.361111115

Calculate the square root of the right side: 3.059593292

Break this problem into two subproblems by setting 
(y + -2.833333334) equal to 3.059593292 and -3.059593292.


Subproblem 1
y + -2.833333334 = 3.059593292

Simplifying
y + -2.833333334 = 3.059593292

Reorder the terms:
-2.833333334 + y = 3.059593292

Solving
-2.833333334 + y = 3.059593292

Solving for variable 'y'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + y = 3.059593292 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + y = 3.059593292 + 2.833333334
y = 3.059593292 + 2.833333334

Combine like terms: 3.059593292 + 2.833333334 = 5.892926626
y = 5.892926626

Simplifying
y = 5.892926626


Subproblem 2
y + -2.833333334 = -3.059593292

Simplifying
y + -2.833333334 = -3.059593292

Reorder the terms:
-2.833333334 + y = -3.059593292

Solving
-2.833333334 + y = -3.059593292

Solving for variable 'y'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + y = -3.059593292 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + y = -3.059593292 + 2.833333334
y = -3.059593292 + 2.833333334

Combine like terms: -3.059593292 + 2.833333334 = -0.226259958
y = -0.226259958

Simplifying
y = -0.226259958


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.892926626, -0.226259958}

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