3m^2-6m=5

Solution for 3m^2-6m=5 equation:

Simplifying
3m2 + -6m = 5

Reorder the terms:
-6m + 3m2 = 5

Solving
-6m + 3m2 = 5

Solving for variable 'm'.

Reorder the terms:
-5 + -6m + 3m2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -6m + 3m2 = 0

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

Divide each side by '3'.
-1.666666667 + -2m + m2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -2m + 1.666666667 + m2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -2m + m2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -2m + m2 = 0 + 1.666666667
-2m + m2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-2m + m2 = 1.666666667

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

Add '1' to each side of the equation.
-2m + 1 + m2 = 1.666666667 + 1

Reorder the terms:
1 + -2m + m2 = 1.666666667 + 1

Combine like terms: 1.666666667 + 1 = 2.666666667
1 + -2m + m2 = 2.666666667

Factor a perfect square on the left side:
(m + -1)(m + -1) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(m + -1) equal to 1.632993162 and -1.632993162.

Subproblem 1
m + -1 = 1.632993162

Simplifying
m + -1 = 1.632993162

Reorder the terms:
-1 + m = 1.632993162

Solving
-1 + m = 1.632993162

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + 1 + m = 1.632993162 + 1

Combine like terms: -1 + 1 = 0
0 + m = 1.632993162 + 1
m = 1.632993162 + 1

Combine like terms: 1.632993162 + 1 = 2.632993162
m = 2.632993162

Simplifying
m = 2.632993162

Subproblem 2
m + -1 = -1.632993162

Simplifying
m + -1 = -1.632993162

Reorder the terms:
-1 + m = -1.632993162

Solving
-1 + m = -1.632993162

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + 1 + m = -1.632993162 + 1

Combine like terms: -1 + 1 = 0
0 + m = -1.632993162 + 1
m = -1.632993162 + 1

Combine like terms: -1.632993162 + 1 = -0.632993162
m = -0.632993162

Simplifying
m = -0.632993162

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.632993162, -0.632993162}