2y^2-39y+17=0

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Solution for 2y^2-39y+17=0 equation: 


Simplifying
2y2 + -39y + 17 = 0

Reorder the terms:
17 + -39y + 2y2 = 0

Solving
17 + -39y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
8.5 + -19.5y + y2 = 0

Move the constant term to the right:

Add '-8.5' to each side of the equation.
8.5 + -19.5y + -8.5 + y2 = 0 + -8.5

Reorder the terms:
8.5 + -8.5 + -19.5y + y2 = 0 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + -19.5y + y2 = 0 + -8.5
-19.5y + y2 = 0 + -8.5

Combine like terms: 0 + -8.5 = -8.5
-19.5y + y2 = -8.5

The y term is -19.5y.  Take half its coefficient (-9.75).
Square it (95.0625) and add it to both sides.

Add '95.0625' to each side of the equation.
-19.5y + 95.0625 + y2 = -8.5 + 95.0625

Reorder the terms:
95.0625 + -19.5y + y2 = -8.5 + 95.0625

Combine like terms: -8.5 + 95.0625 = 86.5625
95.0625 + -19.5y + y2 = 86.5625

Factor a perfect square on the left side:
(y + -9.75)(y + -9.75) = 86.5625

Calculate the square root of the right side: 9.303897033

Break this problem into two subproblems by setting 
(y + -9.75) equal to 9.303897033 and -9.303897033.


Subproblem 1
y + -9.75 = 9.303897033

Simplifying
y + -9.75 = 9.303897033

Reorder the terms:
-9.75 + y = 9.303897033

Solving
-9.75 + y = 9.303897033

Solving for variable 'y'.

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

Add '9.75' to each side of the equation.
-9.75 + 9.75 + y = 9.303897033 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + y = 9.303897033 + 9.75
y = 9.303897033 + 9.75

Combine like terms: 9.303897033 + 9.75 = 19.053897033
y = 19.053897033

Simplifying
y = 19.053897033


Subproblem 2
y + -9.75 = -9.303897033

Simplifying
y + -9.75 = -9.303897033

Reorder the terms:
-9.75 + y = -9.303897033

Solving
-9.75 + y = -9.303897033

Solving for variable 'y'.

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

Add '9.75' to each side of the equation.
-9.75 + 9.75 + y = -9.303897033 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + y = -9.303897033 + 9.75
y = -9.303897033 + 9.75

Combine like terms: -9.303897033 + 9.75 = 0.446102967
y = 0.446102967

Simplifying
y = 0.446102967


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {19.053897033, 0.446102967}

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