3m^2+5m-6=0

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Solution for 3m^2+5m-6=0 equation: 


Simplifying
3m2 + 5m + -6 = 0

Reorder the terms:
-6 + 5m + 3m2 = 0

Solving
-6 + 5m + 3m2 = 0

Solving for variable 'm'.

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

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

Move the constant term to the right:

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

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

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

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

The m term is 1.666666667m.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667m + 0.6944444447 + m2 = 2 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667m + m2 = 2 + 0.6944444447

Combine like terms: 2 + 0.6944444447 = 2.6944444447
0.6944444447 + 1.666666667m + m2 = 2.6944444447

Factor a perfect square on the left side:
(m + 0.8333333335)(m + 0.8333333335) = 2.6944444447

Calculate the square root of the right side: 1.6414763

Break this problem into two subproblems by setting 
(m + 0.8333333335) equal to 1.6414763 and -1.6414763.


Subproblem 1
m + 0.8333333335 = 1.6414763

Simplifying
m + 0.8333333335 = 1.6414763

Reorder the terms:
0.8333333335 + m = 1.6414763

Solving
0.8333333335 + m = 1.6414763

Solving for variable 'm'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + m = 1.6414763 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + m = 1.6414763 + -0.8333333335
m = 1.6414763 + -0.8333333335

Combine like terms: 1.6414763 + -0.8333333335 = 0.8081429665
m = 0.8081429665

Simplifying
m = 0.8081429665


Subproblem 2
m + 0.8333333335 = -1.6414763

Simplifying
m + 0.8333333335 = -1.6414763

Reorder the terms:
0.8333333335 + m = -1.6414763

Solving
0.8333333335 + m = -1.6414763

Solving for variable 'm'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + m = -1.6414763 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + m = -1.6414763 + -0.8333333335
m = -1.6414763 + -0.8333333335

Combine like terms: -1.6414763 + -0.8333333335 = -2.4748096335
m = -2.4748096335

Simplifying
m = -2.4748096335


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.8081429665, -2.4748096335}

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