2y^2=5y+6

Solution for 2y^2=5y+6 equation:

Simplifying
2y2 = 5y + 6

Reorder the terms:
2y2 = 6 + 5y

Solving
2y2 = 6 + 5y

Solving for variable 'y'.

Reorder the terms:
-6 + -5y + 2y2 = 6 + 5y + -6 + -5y

Reorder the terms:
-6 + -5y + 2y2 = 6 + -6 + 5y + -5y

Combine like terms: 6 + -6 = 0
-6 + -5y + 2y2 = 0 + 5y + -5y
-6 + -5y + 2y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-6 + -5y + 2y2 = 0

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

Divide each side by '2'.
-3 + -2.5y + y2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -2.5y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + -2.5y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2.5y + y2 = 0 + 3
-2.5y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
-2.5y + y2 = 3

The y term is -2.5y.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5y + 1.5625 + y2 = 3 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = 3 + 1.5625

Combine like terms: 3 + 1.5625 = 4.5625
1.5625 + -2.5y + y2 = 4.5625

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(y + -1.25) equal to 2.136000936 and -2.136000936.

Subproblem 1
y + -1.25 = 2.136000936

Simplifying
y + -1.25 = 2.136000936

Reorder the terms:
-1.25 + y = 2.136000936

Solving
-1.25 + y = 2.136000936

Solving for variable 'y'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = 2.136000936 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = 2.136000936 + 1.25
y = 2.136000936 + 1.25

Combine like terms: 2.136000936 + 1.25 = 3.386000936
y = 3.386000936

Simplifying
y = 3.386000936

Subproblem 2
y + -1.25 = -2.136000936

Simplifying
y + -1.25 = -2.136000936

Reorder the terms:
-1.25 + y = -2.136000936

Solving
-1.25 + y = -2.136000936

Solving for variable 'y'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = -2.136000936 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = -2.136000936 + 1.25
y = -2.136000936 + 1.25

Combine like terms: -2.136000936 + 1.25 = -0.886000936
y = -0.886000936

Simplifying
y = -0.886000936

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.386000936, -0.886000936}