u^2-6u+4=0

Solution for u^2-6u+4=0 equation:

Simplifying
u2 + -6u + 4 = 0

Reorder the terms:
4 + -6u + u2 = 0

Solving
4 + -6u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -6u + -4 + u2 = 0 + -4

Reorder the terms:
4 + -4 + -6u + u2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -6u + u2 = 0 + -4
-6u + u2 = 0 + -4

Combine like terms: 0 + -4 = -4
-6u + u2 = -4

The u term is -6u.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6u + 9 + u2 = -4 + 9

Reorder the terms:
9 + -6u + u2 = -4 + 9

Combine like terms: -4 + 9 = 5
9 + -6u + u2 = 5

Factor a perfect square on the left side:
(u + -3)(u + -3) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(u + -3) equal to 2.236067978 and -2.236067978.

Subproblem 1
u + -3 = 2.236067978

Simplifying
u + -3 = 2.236067978

Reorder the terms:
-3 + u = 2.236067978

Solving
-3 + u = 2.236067978

Solving for variable 'u'.

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

Add '3' to each side of the equation.
-3 + 3 + u = 2.236067978 + 3

Combine like terms: -3 + 3 = 0
0 + u = 2.236067978 + 3
u = 2.236067978 + 3

Combine like terms: 2.236067978 + 3 = 5.236067978
u = 5.236067978

Simplifying
u = 5.236067978

Subproblem 2
u + -3 = -2.236067978

Simplifying
u + -3 = -2.236067978

Reorder the terms:
-3 + u = -2.236067978

Solving
-3 + u = -2.236067978

Solving for variable 'u'.

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

Add '3' to each side of the equation.
-3 + 3 + u = -2.236067978 + 3

Combine like terms: -3 + 3 = 0
0 + u = -2.236067978 + 3
u = -2.236067978 + 3

Combine like terms: -2.236067978 + 3 = 0.763932022
u = 0.763932022

Simplifying
u = 0.763932022

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {5.236067978, 0.763932022}