7m^2-2m=6

Solution for 7m^2-2m=6 equation:

Simplifying
7m2 + -2m = 6

Reorder the terms:
-2m + 7m2 = 6

Solving
-2m + 7m2 = 6

Solving for variable 'm'.

Reorder the terms:
-6 + -2m + 7m2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -2m + 7m2 = 0

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

Divide each side by '7'.
-0.8571428571 + -0.2857142857m + m2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + -0.2857142857m + 0.8571428571 + m2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + -0.2857142857m + m2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + -0.2857142857m + m2 = 0 + 0.8571428571
-0.2857142857m + m2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
-0.2857142857m + m2 = 0.8571428571

The m term is -0.2857142857m.  Take half its coefficient (-0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
-0.2857142857m + 0.02040816328 + m2 = 0.8571428571 + 0.02040816328

Reorder the terms:
0.02040816328 + -0.2857142857m + m2 = 0.8571428571 + 0.02040816328

Combine like terms: 0.8571428571 + 0.02040816328 = 0.87755102038
0.02040816328 + -0.2857142857m + m2 = 0.87755102038

Factor a perfect square on the left side:
(m + -0.1428571429)(m + -0.1428571429) = 0.87755102038

Calculate the square root of the right side: 0.936776932

Break this problem into two subproblems by setting 
(m + -0.1428571429) equal to 0.936776932 and -0.936776932.

Subproblem 1
m + -0.1428571429 = 0.936776932

Simplifying
m + -0.1428571429 = 0.936776932

Reorder the terms:
-0.1428571429 + m = 0.936776932

Solving
-0.1428571429 + m = 0.936776932

Solving for variable 'm'.

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

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 0.1428571429 + m = 0.936776932 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + m = 0.936776932 + 0.1428571429
m = 0.936776932 + 0.1428571429

Combine like terms: 0.936776932 + 0.1428571429 = 1.0796340749
m = 1.0796340749

Simplifying
m = 1.0796340749

Subproblem 2
m + -0.1428571429 = -0.936776932

Simplifying
m + -0.1428571429 = -0.936776932

Reorder the terms:
-0.1428571429 + m = -0.936776932

Solving
-0.1428571429 + m = -0.936776932

Solving for variable 'm'.

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

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 0.1428571429 + m = -0.936776932 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + m = -0.936776932 + 0.1428571429
m = -0.936776932 + 0.1428571429

Combine like terms: -0.936776932 + 0.1428571429 = -0.7939197891
m = -0.7939197891

Simplifying
m = -0.7939197891

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.0796340749, -0.7939197891}