-1.5+0.5y^2=y

Solution for -1.5+0.5y^2=y equation:

Simplifying
-1.5 + 0.5y2 = y

Solving
-1.5 + 0.5y2 = y

Solving for variable 'y'.

Reorder the terms:
-1.5 + -1y + 0.5y2 = y + -1y

Combine like terms: y + -1y = 0
-1.5 + -1y + 0.5y2 = 0

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

Divide each side by '0.5'.
-3 + -2y + y2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -2y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + -2y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2y + y2 = 0 + 3
-2y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
-2y + y2 = 3

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 3 + 1

Reorder the terms:
1 + -2y + y2 = 3 + 1

Combine like terms: 3 + 1 = 4
1 + -2y + y2 = 4

Factor a perfect square on the left side:
(y + -1)(y + -1) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(y + -1) equal to 2 and -2.

Subproblem 1
y + -1 = 2

Simplifying
y + -1 = 2

Reorder the terms:
-1 + y = 2

Solving
-1 + y = 2

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 2 + 1

Combine like terms: -1 + 1 = 0
0 + y = 2 + 1
y = 2 + 1

Combine like terms: 2 + 1 = 3
y = 3

Simplifying
y = 3

Subproblem 2
y + -1 = -2

Simplifying
y + -1 = -2

Reorder the terms:
-1 + y = -2

Solving
-1 + y = -2

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -2 + 1

Combine like terms: -1 + 1 = 0
0 + y = -2 + 1
y = -2 + 1

Combine like terms: -2 + 1 = -1
y = -1

Simplifying
y = -1

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3, -1}