y^2-3y=5

Solution for y^2-3y=5 equation:

Simplifying
y2 + -3y = 5

Reorder the terms:
-3y + y2 = 5

Solving
-3y + y2 = 5

Solving for variable 'y'.

Reorder the terms:
-5 + -3y + y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -3y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + -3y + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3y + y2 = 0 + 5
-3y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
-3y + y2 = 5

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 = 5 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + -3y + y2 = 7.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(y + -1.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
y + -1.5 = 2.692582404

Simplifying
y + -1.5 = 2.692582404

Reorder the terms:
-1.5 + y = 2.692582404

Solving
-1.5 + y = 2.692582404

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 = 2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 2.692582404 + 1.5
y = 2.692582404 + 1.5

Combine like terms: 2.692582404 + 1.5 = 4.192582404
y = 4.192582404

Simplifying
y = 4.192582404

Subproblem 2
y + -1.5 = -2.692582404

Simplifying
y + -1.5 = -2.692582404

Reorder the terms:
-1.5 + y = -2.692582404

Solving
-1.5 + y = -2.692582404

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 = -2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -2.692582404 + 1.5
y = -2.692582404 + 1.5

Combine like terms: -2.692582404 + 1.5 = -1.192582404
y = -1.192582404

Simplifying
y = -1.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.192582404, -1.192582404}