7y^2-14y+5=0

Solution for 7y^2-14y+5=0 equation:

Simplifying
7y2 + -14y + 5 = 0

Reorder the terms:
5 + -14y + 7y2 = 0

Solving
5 + -14y + 7y2 = 0

Solving for variable 'y'.

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

Divide each side by '7'.
0.7142857143 + -2y + y2 = 0

Move the constant term to the right:

Add '-0.7142857143' to each side of the equation.
0.7142857143 + -2y + -0.7142857143 + y2 = 0 + -0.7142857143

Reorder the terms:
0.7142857143 + -0.7142857143 + -2y + y2 = 0 + -0.7142857143

Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000
0.0000000000 + -2y + y2 = 0 + -0.7142857143
-2y + y2 = 0 + -0.7142857143

Combine like terms: 0 + -0.7142857143 = -0.7142857143
-2y + y2 = -0.7142857143

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 = -0.7142857143 + 1

Reorder the terms:
1 + -2y + y2 = -0.7142857143 + 1

Combine like terms: -0.7142857143 + 1 = 0.2857142857
1 + -2y + y2 = 0.2857142857

Factor a perfect square on the left side:
(y + -1)(y + -1) = 0.2857142857

Calculate the square root of the right side: 0.534522484

Break this problem into two subproblems by setting 
(y + -1) equal to 0.534522484 and -0.534522484.

Subproblem 1
y + -1 = 0.534522484

Simplifying
y + -1 = 0.534522484

Reorder the terms:
-1 + y = 0.534522484

Solving
-1 + y = 0.534522484

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 = 0.534522484 + 1

Combine like terms: -1 + 1 = 0
0 + y = 0.534522484 + 1
y = 0.534522484 + 1

Combine like terms: 0.534522484 + 1 = 1.534522484
y = 1.534522484

Simplifying
y = 1.534522484

Subproblem 2
y + -1 = -0.534522484

Simplifying
y + -1 = -0.534522484

Reorder the terms:
-1 + y = -0.534522484

Solving
-1 + y = -0.534522484

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 = -0.534522484 + 1

Combine like terms: -1 + 1 = 0
0 + y = -0.534522484 + 1
y = -0.534522484 + 1

Combine like terms: -0.534522484 + 1 = 0.465477516
y = 0.465477516

Simplifying
y = 0.465477516

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.534522484, 0.465477516}