3y^2-50y+17=0

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Solution for 3y^2-50y+17=0 equation: 


Simplifying
3y2 + -50y + 17 = 0

Reorder the terms:
17 + -50y + 3y2 = 0

Solving
17 + -50y + 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'.
5.666666667 + -16.66666667y + y2 = 0

Move the constant term to the right:

Add '-5.666666667' to each side of the equation.
5.666666667 + -16.66666667y + -5.666666667 + y2 = 0 + -5.666666667

Reorder the terms:
5.666666667 + -5.666666667 + -16.66666667y + y2 = 0 + -5.666666667

Combine like terms: 5.666666667 + -5.666666667 = 0.000000000
0.000000000 + -16.66666667y + y2 = 0 + -5.666666667
-16.66666667y + y2 = 0 + -5.666666667

Combine like terms: 0 + -5.666666667 = -5.666666667
-16.66666667y + y2 = -5.666666667

The y term is -16.66666667y.  Take half its coefficient (-8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
-16.66666667y + 69.44444447 + y2 = -5.666666667 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667y + y2 = -5.666666667 + 69.44444447

Combine like terms: -5.666666667 + 69.44444447 = 63.777777803
69.44444447 + -16.66666667y + y2 = 63.777777803

Factor a perfect square on the left side:
(y + -8.333333335)(y + -8.333333335) = 63.777777803

Calculate the square root of the right side: 7.986099035

Break this problem into two subproblems by setting 
(y + -8.333333335) equal to 7.986099035 and -7.986099035.


Subproblem 1
y + -8.333333335 = 7.986099035

Simplifying
y + -8.333333335 = 7.986099035

Reorder the terms:
-8.333333335 + y = 7.986099035

Solving
-8.333333335 + y = 7.986099035

Solving for variable 'y'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + y = 7.986099035 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + y = 7.986099035 + 8.333333335
y = 7.986099035 + 8.333333335

Combine like terms: 7.986099035 + 8.333333335 = 16.31943237
y = 16.31943237

Simplifying
y = 16.31943237


Subproblem 2
y + -8.333333335 = -7.986099035

Simplifying
y + -8.333333335 = -7.986099035

Reorder the terms:
-8.333333335 + y = -7.986099035

Solving
-8.333333335 + y = -7.986099035

Solving for variable 'y'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + y = -7.986099035 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + y = -7.986099035 + 8.333333335
y = -7.986099035 + 8.333333335

Combine like terms: -7.986099035 + 8.333333335 = 0.3472343
y = 0.3472343

Simplifying
y = 0.3472343


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {16.31943237, 0.3472343}

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