5v^2+16v+6=0

Solution for 5v^2+16v+6=0 equation:

Simplifying
5v2 + 16v + 6 = 0

Reorder the terms:
6 + 16v + 5v2 = 0

Solving
6 + 16v + 5v2 = 0

Solving for variable 'v'.

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

Divide each side by '5'.
1.2 + 3.2v + v2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 3.2v + -1.2 + v2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 3.2v + v2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 3.2v + v2 = 0 + -1.2
3.2v + v2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
3.2v + v2 = -1.2

The v term is 3.2v.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2v + 2.56 + v2 = -1.2 + 2.56

Reorder the terms:
2.56 + 3.2v + v2 = -1.2 + 2.56

Combine like terms: -1.2 + 2.56 = 1.36
2.56 + 3.2v + v2 = 1.36

Factor a perfect square on the left side:
(v + 1.6)(v + 1.6) = 1.36

Calculate the square root of the right side: 1.166190379

Break this problem into two subproblems by setting 
(v + 1.6) equal to 1.166190379 and -1.166190379.

Subproblem 1
v + 1.6 = 1.166190379

Simplifying
v + 1.6 = 1.166190379

Reorder the terms:
1.6 + v = 1.166190379

Solving
1.6 + v = 1.166190379

Solving for variable 'v'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + v = 1.166190379 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + v = 1.166190379 + -1.6
v = 1.166190379 + -1.6

Combine like terms: 1.166190379 + -1.6 = -0.433809621
v = -0.433809621

Simplifying
v = -0.433809621

Subproblem 2
v + 1.6 = -1.166190379

Simplifying
v + 1.6 = -1.166190379

Reorder the terms:
1.6 + v = -1.166190379

Solving
1.6 + v = -1.166190379

Solving for variable 'v'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + v = -1.166190379 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + v = -1.166190379 + -1.6
v = -1.166190379 + -1.6

Combine like terms: -1.166190379 + -1.6 = -2.766190379
v = -2.766190379

Simplifying
v = -2.766190379

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.433809621, -2.766190379}