3u^2=6u+1

Solution for 3u^2=6u+1 equation:

Simplifying
3u2 = 6u + 1

Reorder the terms:
3u2 = 1 + 6u

Solving
3u2 = 1 + 6u

Solving for variable 'u'.

Reorder the terms:
-1 + -6u + 3u2 = 1 + 6u + -1 + -6u

Reorder the terms:
-1 + -6u + 3u2 = 1 + -1 + 6u + -6u

Combine like terms: 1 + -1 = 0
-1 + -6u + 3u2 = 0 + 6u + -6u
-1 + -6u + 3u2 = 6u + -6u

Combine like terms: 6u + -6u = 0
-1 + -6u + 3u2 = 0

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

Divide each side by '3'.
-0.3333333333 + -2u + u2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -2u + 0.3333333333 + u2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -2u + u2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -2u + u2 = 0 + 0.3333333333
-2u + u2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-2u + u2 = 0.3333333333

The u term is -2u.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2u + 1 + u2 = 0.3333333333 + 1

Reorder the terms:
1 + -2u + u2 = 0.3333333333 + 1

Combine like terms: 0.3333333333 + 1 = 1.3333333333
1 + -2u + u2 = 1.3333333333

Factor a perfect square on the left side:
(u + -1)(u + -1) = 1.3333333333

Calculate the square root of the right side: 1.154700538

Break this problem into two subproblems by setting 
(u + -1) equal to 1.154700538 and -1.154700538.

Subproblem 1
u + -1 = 1.154700538

Simplifying
u + -1 = 1.154700538

Reorder the terms:
-1 + u = 1.154700538

Solving
-1 + u = 1.154700538

Solving for variable 'u'.

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

Add '1' to each side of the equation.
-1 + 1 + u = 1.154700538 + 1

Combine like terms: -1 + 1 = 0
0 + u = 1.154700538 + 1
u = 1.154700538 + 1

Combine like terms: 1.154700538 + 1 = 2.154700538
u = 2.154700538

Simplifying
u = 2.154700538

Subproblem 2
u + -1 = -1.154700538

Simplifying
u + -1 = -1.154700538

Reorder the terms:
-1 + u = -1.154700538

Solving
-1 + u = -1.154700538

Solving for variable 'u'.

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

Add '1' to each side of the equation.
-1 + 1 + u = -1.154700538 + 1

Combine like terms: -1 + 1 = 0
0 + u = -1.154700538 + 1
u = -1.154700538 + 1

Combine like terms: -1.154700538 + 1 = -0.154700538
u = -0.154700538

Simplifying
u = -0.154700538

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {2.154700538, -0.154700538}