3u^2=6u+78

Solution for 3u^2=6u+78 equation:

Simplifying
3u2 = 6u + 78

Reorder the terms:
3u2 = 78 + 6u

Solving
3u2 = 78 + 6u

Solving for variable 'u'.

Reorder the terms:
-78 + -6u + 3u2 = 78 + 6u + -78 + -6u

Reorder the terms:
-78 + -6u + 3u2 = 78 + -78 + 6u + -6u

Combine like terms: 78 + -78 = 0
-78 + -6u + 3u2 = 0 + 6u + -6u
-78 + -6u + 3u2 = 6u + -6u

Combine like terms: 6u + -6u = 0
-78 + -6u + 3u2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-26 + -2u + u2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-26 + -2u + u2)' equal to zero and attempt to solve:

Simplifying
-26 + -2u + u2 = 0

Solving
-26 + -2u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + -2u + 26 + u2 = 0 + 26

Reorder the terms:
-26 + 26 + -2u + u2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -2u + u2 = 0 + 26
-2u + u2 = 0 + 26

Combine like terms: 0 + 26 = 26
-2u + u2 = 26

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 = 26 + 1

Reorder the terms:
1 + -2u + u2 = 26 + 1

Combine like terms: 26 + 1 = 27
1 + -2u + u2 = 27

Factor a perfect square on the left side:
(u + -1)(u + -1) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(u + -1) equal to 5.196152423 and -5.196152423.

Subproblem 1
u + -1 = 5.196152423

Simplifying
u + -1 = 5.196152423

Reorder the terms:
-1 + u = 5.196152423

Solving
-1 + u = 5.196152423

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 = 5.196152423 + 1

Combine like terms: -1 + 1 = 0
0 + u = 5.196152423 + 1
u = 5.196152423 + 1

Combine like terms: 5.196152423 + 1 = 6.196152423
u = 6.196152423

Simplifying
u = 6.196152423

Subproblem 2
u + -1 = -5.196152423

Simplifying
u + -1 = -5.196152423

Reorder the terms:
-1 + u = -5.196152423

Solving
-1 + u = -5.196152423

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 = -5.196152423 + 1

Combine like terms: -1 + 1 = 0
0 + u = -5.196152423 + 1
u = -5.196152423 + 1

Combine like terms: -5.196152423 + 1 = -4.196152423
u = -4.196152423

Simplifying
u = -4.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {6.196152423, -4.196152423}
Solution
u = {6.196152423, -4.196152423}