5y^2-148=y

Solution for 5y^2-148=y equation:

Simplifying
5y2 + -148 = y

Reorder the terms:
-148 + 5y2 = y

Solving
-148 + 5y2 = y

Solving for variable 'y'.

Reorder the terms:
-148 + -1y + 5y2 = y + -1y

Combine like terms: y + -1y = 0
-148 + -1y + 5y2 = 0

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

Divide each side by '5'.
-29.6 + -0.2y + y2 = 0

Move the constant term to the right:

Add '29.6' to each side of the equation.
-29.6 + -0.2y + 29.6 + y2 = 0 + 29.6

Reorder the terms:
-29.6 + 29.6 + -0.2y + y2 = 0 + 29.6

Combine like terms: -29.6 + 29.6 = 0.0
0.0 + -0.2y + y2 = 0 + 29.6
-0.2y + y2 = 0 + 29.6

Combine like terms: 0 + 29.6 = 29.6
-0.2y + y2 = 29.6

The y term is -0.2y.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2y + 0.01 + y2 = 29.6 + 0.01

Reorder the terms:
0.01 + -0.2y + y2 = 29.6 + 0.01

Combine like terms: 29.6 + 0.01 = 29.61
0.01 + -0.2y + y2 = 29.61

Factor a perfect square on the left side:
(y + -0.1)(y + -0.1) = 29.61

Calculate the square root of the right side: 5.441507144

Break this problem into two subproblems by setting 
(y + -0.1) equal to 5.441507144 and -5.441507144.

Subproblem 1
y + -0.1 = 5.441507144

Simplifying
y + -0.1 = 5.441507144

Reorder the terms:
-0.1 + y = 5.441507144

Solving
-0.1 + y = 5.441507144

Solving for variable 'y'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + y = 5.441507144 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + y = 5.441507144 + 0.1
y = 5.441507144 + 0.1

Combine like terms: 5.441507144 + 0.1 = 5.541507144
y = 5.541507144

Simplifying
y = 5.541507144

Subproblem 2
y + -0.1 = -5.441507144

Simplifying
y + -0.1 = -5.441507144

Reorder the terms:
-0.1 + y = -5.441507144

Solving
-0.1 + y = -5.441507144

Solving for variable 'y'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + y = -5.441507144 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + y = -5.441507144 + 0.1
y = -5.441507144 + 0.1

Combine like terms: -5.441507144 + 0.1 = -5.341507144
y = -5.341507144

Simplifying
y = -5.341507144

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.541507144, -5.341507144}