-9m^2+4m+8=0

Solution for -9m^2+4m+8=0 equation:

Simplifying
-9m2 + 4m + 8 = 0

Reorder the terms:
8 + 4m + -9m2 = 0

Solving
8 + 4m + -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 + -0.4444444444m + m2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + -0.4444444444m + 0.8888888889 + m2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + -0.4444444444m + m2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + -0.4444444444m + m2 = 0 + 0.8888888889
-0.4444444444m + m2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
-0.4444444444m + m2 = 0.8888888889

The m term is -0.4444444444m.  Take half its coefficient (-0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
-0.4444444444m + 0.04938271604 + m2 = 0.8888888889 + 0.04938271604

Reorder the terms:
0.04938271604 + -0.4444444444m + m2 = 0.8888888889 + 0.04938271604

Combine like terms: 0.8888888889 + 0.04938271604 = 0.93827160494
0.04938271604 + -0.4444444444m + m2 = 0.93827160494

Factor a perfect square on the left side:
(m + -0.2222222222)(m + -0.2222222222) = 0.93827160494

Calculate the square root of the right side: 0.96864421

Break this problem into two subproblems by setting 
(m + -0.2222222222) equal to 0.96864421 and -0.96864421.

Subproblem 1
m + -0.2222222222 = 0.96864421

Simplifying
m + -0.2222222222 = 0.96864421

Reorder the terms:
-0.2222222222 + m = 0.96864421

Solving
-0.2222222222 + m = 0.96864421

Solving for variable 'm'.

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

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.2222222222 + m = 0.96864421 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + m = 0.96864421 + 0.2222222222
m = 0.96864421 + 0.2222222222

Combine like terms: 0.96864421 + 0.2222222222 = 1.1908664322
m = 1.1908664322

Simplifying
m = 1.1908664322

Subproblem 2
m + -0.2222222222 = -0.96864421

Simplifying
m + -0.2222222222 = -0.96864421

Reorder the terms:
-0.2222222222 + m = -0.96864421

Solving
-0.2222222222 + m = -0.96864421

Solving for variable 'm'.

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

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.2222222222 + m = -0.96864421 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + m = -0.96864421 + 0.2222222222
m = -0.96864421 + 0.2222222222

Combine like terms: -0.96864421 + 0.2222222222 = -0.7464219878
m = -0.7464219878

Simplifying
m = -0.7464219878

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {1.1908664322, -0.7464219878}