9m^2-24m+8=0

Solution for 9m^2-24m+8=0 equation:

Simplifying
9m2 + -24m + 8 = 0

Reorder the terms:
8 + -24m + 9m2 = 0

Solving
8 + -24m + 9m2 = 0

Solving for variable 'm'.

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

Divide each side by '9'.
0.8888888889 + -2.666666667m + m2 = 0

Move the constant term to the right:

Add '-0.8888888889' to each side of the equation.
0.8888888889 + -2.666666667m + -0.8888888889 + m2 = 0 + -0.8888888889

Reorder the terms:
0.8888888889 + -0.8888888889 + -2.666666667m + m2 = 0 + -0.8888888889

Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000
0.0000000000 + -2.666666667m + m2 = 0 + -0.8888888889
-2.666666667m + m2 = 0 + -0.8888888889

Combine like terms: 0 + -0.8888888889 = -0.8888888889
-2.666666667m + m2 = -0.8888888889

The m term is -2.666666667m.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667m + 1.777777780 + m2 = -0.8888888889 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667m + m2 = -0.8888888889 + 1.777777780

Combine like terms: -0.8888888889 + 1.777777780 = 0.8888888911
1.777777780 + -2.666666667m + m2 = 0.8888888911

Factor a perfect square on the left side:
(m + -1.333333334)(m + -1.333333334) = 0.8888888911

Calculate the square root of the right side: 0.942809043

Break this problem into two subproblems by setting 
(m + -1.333333334) equal to 0.942809043 and -0.942809043.

Subproblem 1
m + -1.333333334 = 0.942809043

Simplifying
m + -1.333333334 = 0.942809043

Reorder the terms:
-1.333333334 + m = 0.942809043

Solving
-1.333333334 + m = 0.942809043

Solving for variable 'm'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + m = 0.942809043 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + m = 0.942809043 + 1.333333334
m = 0.942809043 + 1.333333334

Combine like terms: 0.942809043 + 1.333333334 = 2.276142377
m = 2.276142377

Simplifying
m = 2.276142377

Subproblem 2
m + -1.333333334 = -0.942809043

Simplifying
m + -1.333333334 = -0.942809043

Reorder the terms:
-1.333333334 + m = -0.942809043

Solving
-1.333333334 + m = -0.942809043

Solving for variable 'm'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + m = -0.942809043 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + m = -0.942809043 + 1.333333334
m = -0.942809043 + 1.333333334

Combine like terms: -0.942809043 + 1.333333334 = 0.390524291
m = 0.390524291

Simplifying
m = 0.390524291

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {2.276142377, 0.390524291}