7y^2-14y+15=114

Solution for 7y^2-14y+15=114 equation:

Simplifying
7y2 + -14y + 15 = 114

Reorder the terms:
15 + -14y + 7y2 = 114

Solving
15 + -14y + 7y2 = 114

Solving for variable 'y'.

Reorder the terms:
15 + -114 + -14y + 7y2 = 114 + -114

Combine like terms: 15 + -114 = -99
-99 + -14y + 7y2 = 114 + -114

Combine like terms: 114 + -114 = 0
-99 + -14y + 7y2 = 0

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

Divide each side by '7'.
-14.14285714 + -2y + y2 = 0

Move the constant term to the right:

Add '14.14285714' to each side of the equation.
-14.14285714 + -2y + 14.14285714 + y2 = 0 + 14.14285714

Reorder the terms:
-14.14285714 + 14.14285714 + -2y + y2 = 0 + 14.14285714

Combine like terms: -14.14285714 + 14.14285714 = 0.00000000
0.00000000 + -2y + y2 = 0 + 14.14285714
-2y + y2 = 0 + 14.14285714

Combine like terms: 0 + 14.14285714 = 14.14285714
-2y + y2 = 14.14285714

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 = 14.14285714 + 1

Reorder the terms:
1 + -2y + y2 = 14.14285714 + 1

Combine like terms: 14.14285714 + 1 = 15.14285714
1 + -2y + y2 = 15.14285714

Factor a perfect square on the left side:
(y + -1)(y + -1) = 15.14285714

Calculate the square root of the right side: 3.89138242

Break this problem into two subproblems by setting 
(y + -1) equal to 3.89138242 and -3.89138242.

Subproblem 1
y + -1 = 3.89138242

Simplifying
y + -1 = 3.89138242

Reorder the terms:
-1 + y = 3.89138242

Solving
-1 + y = 3.89138242

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 = 3.89138242 + 1

Combine like terms: -1 + 1 = 0
0 + y = 3.89138242 + 1
y = 3.89138242 + 1

Combine like terms: 3.89138242 + 1 = 4.89138242
y = 4.89138242

Simplifying
y = 4.89138242

Subproblem 2
y + -1 = -3.89138242

Simplifying
y + -1 = -3.89138242

Reorder the terms:
-1 + y = -3.89138242

Solving
-1 + y = -3.89138242

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 = -3.89138242 + 1

Combine like terms: -1 + 1 = 0
0 + y = -3.89138242 + 1
y = -3.89138242 + 1

Combine like terms: -3.89138242 + 1 = -2.89138242
y = -2.89138242

Simplifying
y = -2.89138242

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.89138242, -2.89138242}