2y^2-6y-38=0

Solution for 2y^2-6y-38=0 equation:

Simplifying
2y2 + -6y + -38 = 0

Reorder the terms:
-38 + -6y + 2y2 = 0

Solving
-38 + -6y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + -3y + y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-19 + -3y + y2)' equal to zero and attempt to solve:

Simplifying
-19 + -3y + y2 = 0

Solving
-19 + -3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -3y + 19 + y2 = 0 + 19

Reorder the terms:
-19 + 19 + -3y + y2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -3y + y2 = 0 + 19
-3y + y2 = 0 + 19

Combine like terms: 0 + 19 = 19
-3y + y2 = 19

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 19 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 19 + 2.25

Combine like terms: 19 + 2.25 = 21.25
2.25 + -3y + y2 = 21.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(y + -1.5) equal to 4.609772229 and -4.609772229.

Subproblem 1
y + -1.5 = 4.609772229

Simplifying
y + -1.5 = 4.609772229

Reorder the terms:
-1.5 + y = 4.609772229

Solving
-1.5 + y = 4.609772229

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 4.609772229 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 4.609772229 + 1.5
y = 4.609772229 + 1.5

Combine like terms: 4.609772229 + 1.5 = 6.109772229
y = 6.109772229

Simplifying
y = 6.109772229

Subproblem 2
y + -1.5 = -4.609772229

Simplifying
y + -1.5 = -4.609772229

Reorder the terms:
-1.5 + y = -4.609772229

Solving
-1.5 + y = -4.609772229

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -4.609772229 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -4.609772229 + 1.5
y = -4.609772229 + 1.5

Combine like terms: -4.609772229 + 1.5 = -3.109772229
y = -3.109772229

Simplifying
y = -3.109772229

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.109772229, -3.109772229}
Solution
y = {6.109772229, -3.109772229}