y^2-15.2y+52=0

Solution for y^2-15.2y+52=0 equation:

Simplifying
y2 + -15.2y + 52 = 0

Reorder the terms:
52 + -15.2y + y2 = 0

Solving
52 + -15.2y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-52' to each side of the equation.
52 + -15.2y + -52 + y2 = 0 + -52

Reorder the terms:
52 + -52 + -15.2y + y2 = 0 + -52

Combine like terms: 52 + -52 = 0
0 + -15.2y + y2 = 0 + -52
-15.2y + y2 = 0 + -52

Combine like terms: 0 + -52 = -52
-15.2y + y2 = -52

The y term is -15.2y.  Take half its coefficient (-7.6).
Square it (57.76) and add it to both sides.

Add '57.76' to each side of the equation.
-15.2y + 57.76 + y2 = -52 + 57.76

Reorder the terms:
57.76 + -15.2y + y2 = -52 + 57.76

Combine like terms: -52 + 57.76 = 5.76
57.76 + -15.2y + y2 = 5.76

Factor a perfect square on the left side:
(y + -7.6)(y + -7.6) = 5.76

Calculate the square root of the right side: 2.4

Break this problem into two subproblems by setting 
(y + -7.6) equal to 2.4 and -2.4.

Subproblem 1
y + -7.6 = 2.4

Simplifying
y + -7.6 = 2.4

Reorder the terms:
-7.6 + y = 2.4

Solving
-7.6 + y = 2.4

Solving for variable 'y'.

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

Add '7.6' to each side of the equation.
-7.6 + 7.6 + y = 2.4 + 7.6

Combine like terms: -7.6 + 7.6 = 0.0
0.0 + y = 2.4 + 7.6
y = 2.4 + 7.6

Combine like terms: 2.4 + 7.6 = 10
y = 10

Simplifying
y = 10

Subproblem 2
y + -7.6 = -2.4

Simplifying
y + -7.6 = -2.4

Reorder the terms:
-7.6 + y = -2.4

Solving
-7.6 + y = -2.4

Solving for variable 'y'.

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

Add '7.6' to each side of the equation.
-7.6 + 7.6 + y = -2.4 + 7.6

Combine like terms: -7.6 + 7.6 = 0.0
0.0 + y = -2.4 + 7.6
y = -2.4 + 7.6

Combine like terms: -2.4 + 7.6 = 5.2
y = 5.2

Simplifying
y = 5.2

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10, 5.2}