y^2-8y+3=0

Solution for y^2-8y+3=0 equation:

Simplifying
y2 + -8y + 3 = 0

Reorder the terms:
3 + -8y + y2 = 0

Solving
3 + -8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -8y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + -8y + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8y + y2 = 0 + -3
-8y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-8y + y2 = -3

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = -3 + 16

Reorder the terms:
16 + -8y + y2 = -3 + 16

Combine like terms: -3 + 16 = 13
16 + -8y + y2 = 13

Factor a perfect square on the left side:
(y + -4)(y + -4) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(y + -4) equal to 3.605551275 and -3.605551275.

Subproblem 1
y + -4 = 3.605551275

Simplifying
y + -4 = 3.605551275

Reorder the terms:
-4 + y = 3.605551275

Solving
-4 + y = 3.605551275

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = 3.605551275 + 4

Combine like terms: -4 + 4 = 0
0 + y = 3.605551275 + 4
y = 3.605551275 + 4

Combine like terms: 3.605551275 + 4 = 7.605551275
y = 7.605551275

Simplifying
y = 7.605551275

Subproblem 2
y + -4 = -3.605551275

Simplifying
y + -4 = -3.605551275

Reorder the terms:
-4 + y = -3.605551275

Solving
-4 + y = -3.605551275

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = -3.605551275 + 4

Combine like terms: -4 + 4 = 0
0 + y = -3.605551275 + 4
y = -3.605551275 + 4

Combine like terms: -3.605551275 + 4 = 0.394448725
y = 0.394448725

Simplifying
y = 0.394448725

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.605551275, 0.394448725}