0=y^2-3y+1.25

Solution for 0=y^2-3y+1.25 equation:

Simplifying
0 = y2 + -3y + 1.25

Reorder the terms:
0 = 1.25 + -3y + y2

Solving
0 = 1.25 + -3y + y2

Solving for variable 'y'.

Combine like terms: 0 + -1.25 = -1.25
-1.25 + 3y + -1y2 = 1.25 + -3y + y2 + -1.25 + 3y + -1y2

Reorder the terms:
-1.25 + 3y + -1y2 = 1.25 + -1.25 + -3y + 3y + y2 + -1y2

Combine like terms: 1.25 + -1.25 = 0.00
-1.25 + 3y + -1y2 = 0.00 + -3y + 3y + y2 + -1y2
-1.25 + 3y + -1y2 = -3y + 3y + y2 + -1y2

Combine like terms: -3y + 3y = 0
-1.25 + 3y + -1y2 = 0 + y2 + -1y2
-1.25 + 3y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-1.25 + 3y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1.25 + -3y + y2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -3y + -1.25 + y2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -3y + y2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -3y + y2 = 0 + -1.25
-3y + y2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-3y + y2 = -1.25

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 = -1.25 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -1.25 + 2.25

Combine like terms: -1.25 + 2.25 = 1
2.25 + -3y + y2 = 1

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(y + -1.5) equal to 1 and -1.

Subproblem 1
y + -1.5 = 1

Simplifying
y + -1.5 = 1

Reorder the terms:
-1.5 + y = 1

Solving
-1.5 + y = 1

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 = 1 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 1 + 1.5
y = 1 + 1.5

Combine like terms: 1 + 1.5 = 2.5
y = 2.5

Simplifying
y = 2.5

Subproblem 2
y + -1.5 = -1

Simplifying
y + -1.5 = -1

Reorder the terms:
-1.5 + y = -1

Solving
-1.5 + y = -1

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 = -1 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -1 + 1.5
y = -1 + 1.5

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

Simplifying
y = 0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.5, 0.5}