y=5y^2-14y+8

Solution for y=5y^2-14y+8 equation:

Simplifying
y = 5y2 + -14y + 8

Reorder the terms:
y = 8 + -14y + 5y2

Solving
y = 8 + -14y + 5y2

Solving for variable 'y'.

Reorder the terms:
-8 + y + 14y + -5y2 = 8 + -14y + 5y2 + -8 + 14y + -5y2

Combine like terms: y + 14y = 15y
-8 + 15y + -5y2 = 8 + -14y + 5y2 + -8 + 14y + -5y2

Reorder the terms:
-8 + 15y + -5y2 = 8 + -8 + -14y + 14y + 5y2 + -5y2

Combine like terms: 8 + -8 = 0
-8 + 15y + -5y2 = 0 + -14y + 14y + 5y2 + -5y2
-8 + 15y + -5y2 = -14y + 14y + 5y2 + -5y2

Combine like terms: -14y + 14y = 0
-8 + 15y + -5y2 = 0 + 5y2 + -5y2
-8 + 15y + -5y2 = 5y2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
-8 + 15y + -5y2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
1.6 + -3y + y2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + -3y + -1.6 + y2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + -3y + y2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + -3y + y2 = 0 + -1.6
-3y + y2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
-3y + y2 = -1.6

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 = -1.6 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -1.6 + 2.25

Combine like terms: -1.6 + 2.25 = 0.65
2.25 + -3y + y2 = 0.65

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 0.65

Calculate the square root of the right side: 0.806225775

Break this problem into two subproblems by setting 
(y + -1.5) equal to 0.806225775 and -0.806225775.

Subproblem 1
y + -1.5 = 0.806225775

Simplifying
y + -1.5 = 0.806225775

Reorder the terms:
-1.5 + y = 0.806225775

Solving
-1.5 + y = 0.806225775

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 = 0.806225775 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 0.806225775 + 1.5
y = 0.806225775 + 1.5

Combine like terms: 0.806225775 + 1.5 = 2.306225775
y = 2.306225775

Simplifying
y = 2.306225775

Subproblem 2
y + -1.5 = -0.806225775

Simplifying
y + -1.5 = -0.806225775

Reorder the terms:
-1.5 + y = -0.806225775

Solving
-1.5 + y = -0.806225775

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 = -0.806225775 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -0.806225775 + 1.5
y = -0.806225775 + 1.5

Combine like terms: -0.806225775 + 1.5 = 0.693774225
y = 0.693774225

Simplifying
y = 0.693774225

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.306225775, 0.693774225}