2m^2+17m+6=0

Solution for 2m^2+17m+6=0 equation:

Simplifying
2m2 + 17m + 6 = 0

Reorder the terms:
6 + 17m + 2m2 = 0

Solving
6 + 17m + 2m2 = 0

Solving for variable 'm'.

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

Divide each side by '2'.
3 + 8.5m + m2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 8.5m + -3 + m2 = 0 + -3

Reorder the terms:
3 + -3 + 8.5m + m2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8.5m + m2 = 0 + -3
8.5m + m2 = 0 + -3

Combine like terms: 0 + -3 = -3
8.5m + m2 = -3

The m term is 8.5m.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5m + 18.0625 + m2 = -3 + 18.0625

Reorder the terms:
18.0625 + 8.5m + m2 = -3 + 18.0625

Combine like terms: -3 + 18.0625 = 15.0625
18.0625 + 8.5m + m2 = 15.0625

Factor a perfect square on the left side:
(m + 4.25)(m + 4.25) = 15.0625

Calculate the square root of the right side: 3.881043674

Break this problem into two subproblems by setting 
(m + 4.25) equal to 3.881043674 and -3.881043674.

Subproblem 1
m + 4.25 = 3.881043674

Simplifying
m + 4.25 = 3.881043674

Reorder the terms:
4.25 + m = 3.881043674

Solving
4.25 + m = 3.881043674

Solving for variable 'm'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + m = 3.881043674 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + m = 3.881043674 + -4.25
m = 3.881043674 + -4.25

Combine like terms: 3.881043674 + -4.25 = -0.368956326
m = -0.368956326

Simplifying
m = -0.368956326

Subproblem 2
m + 4.25 = -3.881043674

Simplifying
m + 4.25 = -3.881043674

Reorder the terms:
4.25 + m = -3.881043674

Solving
4.25 + m = -3.881043674

Solving for variable 'm'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + m = -3.881043674 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + m = -3.881043674 + -4.25
m = -3.881043674 + -4.25

Combine like terms: -3.881043674 + -4.25 = -8.131043674
m = -8.131043674

Simplifying
m = -8.131043674

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-0.368956326, -8.131043674}