5m^2+25m-6=0

Solution for 5m^2+25m-6=0 equation:

Simplifying
5m2 + 25m + -6 = 0

Reorder the terms:
-6 + 25m + 5m2 = 0

Solving
-6 + 25m + 5m2 = 0

Solving for variable 'm'.

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

Divide each side by '5'.
-1.2 + 5m + m2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 5m + 1.2 + m2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 5m + m2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 5m + m2 = 0 + 1.2
5m + m2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
5m + m2 = 1.2

The m term is 5m.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5m + 6.25 + m2 = 1.2 + 6.25

Reorder the terms:
6.25 + 5m + m2 = 1.2 + 6.25

Combine like terms: 1.2 + 6.25 = 7.45
6.25 + 5m + m2 = 7.45

Factor a perfect square on the left side:
(m + 2.5)(m + 2.5) = 7.45

Calculate the square root of the right side: 2.729468813

Break this problem into two subproblems by setting 
(m + 2.5) equal to 2.729468813 and -2.729468813.

Subproblem 1
m + 2.5 = 2.729468813

Simplifying
m + 2.5 = 2.729468813

Reorder the terms:
2.5 + m = 2.729468813

Solving
2.5 + m = 2.729468813

Solving for variable 'm'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + m = 2.729468813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + m = 2.729468813 + -2.5
m = 2.729468813 + -2.5

Combine like terms: 2.729468813 + -2.5 = 0.229468813
m = 0.229468813

Simplifying
m = 0.229468813

Subproblem 2
m + 2.5 = -2.729468813

Simplifying
m + 2.5 = -2.729468813

Reorder the terms:
2.5 + m = -2.729468813

Solving
2.5 + m = -2.729468813

Solving for variable 'm'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + m = -2.729468813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + m = -2.729468813 + -2.5
m = -2.729468813 + -2.5

Combine like terms: -2.729468813 + -2.5 = -5.229468813
m = -5.229468813

Simplifying
m = -5.229468813

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.229468813, -5.229468813}