5y^2=26y+5

Solution for 5y^2=26y+5 equation:

Simplifying
5y2 = 26y + 5

Reorder the terms:
5y2 = 5 + 26y

Solving
5y2 = 5 + 26y

Solving for variable 'y'.

Reorder the terms:
-5 + -26y + 5y2 = 5 + 26y + -5 + -26y

Reorder the terms:
-5 + -26y + 5y2 = 5 + -5 + 26y + -26y

Combine like terms: 5 + -5 = 0
-5 + -26y + 5y2 = 0 + 26y + -26y
-5 + -26y + 5y2 = 26y + -26y

Combine like terms: 26y + -26y = 0
-5 + -26y + 5y2 = 0

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

Divide each side by '5'.
-1 + -5.2y + y2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -5.2y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + -5.2y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5.2y + y2 = 0 + 1
-5.2y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
-5.2y + y2 = 1

The y term is -5.2y.  Take half its coefficient (-2.6).
Square it (6.76) and add it to both sides.

Add '6.76' to each side of the equation.
-5.2y + 6.76 + y2 = 1 + 6.76

Reorder the terms:
6.76 + -5.2y + y2 = 1 + 6.76

Combine like terms: 1 + 6.76 = 7.76
6.76 + -5.2y + y2 = 7.76

Factor a perfect square on the left side:
(y + -2.6)(y + -2.6) = 7.76

Calculate the square root of the right side: 2.785677655

Break this problem into two subproblems by setting 
(y + -2.6) equal to 2.785677655 and -2.785677655.

Subproblem 1
y + -2.6 = 2.785677655

Simplifying
y + -2.6 = 2.785677655

Reorder the terms:
-2.6 + y = 2.785677655

Solving
-2.6 + y = 2.785677655

Solving for variable 'y'.

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

Add '2.6' to each side of the equation.
-2.6 + 2.6 + y = 2.785677655 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + y = 2.785677655 + 2.6
y = 2.785677655 + 2.6

Combine like terms: 2.785677655 + 2.6 = 5.385677655
y = 5.385677655

Simplifying
y = 5.385677655

Subproblem 2
y + -2.6 = -2.785677655

Simplifying
y + -2.6 = -2.785677655

Reorder the terms:
-2.6 + y = -2.785677655

Solving
-2.6 + y = -2.785677655

Solving for variable 'y'.

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

Add '2.6' to each side of the equation.
-2.6 + 2.6 + y = -2.785677655 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + y = -2.785677655 + 2.6
y = -2.785677655 + 2.6

Combine like terms: -2.785677655 + 2.6 = -0.185677655
y = -0.185677655

Simplifying
y = -0.185677655

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.385677655, -0.185677655}