5w^2+30w+6=0

Solution for 5w^2+30w+6=0 equation:

Simplifying
5w2 + 30w + 6 = 0

Reorder the terms:
6 + 30w + 5w2 = 0

Solving
6 + 30w + 5w2 = 0

Solving for variable 'w'.

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

Divide each side by '5'.
1.2 + 6w + w2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 6w + -1.2 + w2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 6w + w2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 6w + w2 = 0 + -1.2
6w + w2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
6w + w2 = -1.2

The w term is 6w.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6w + 9 + w2 = -1.2 + 9

Reorder the terms:
9 + 6w + w2 = -1.2 + 9

Combine like terms: -1.2 + 9 = 7.8
9 + 6w + w2 = 7.8

Factor a perfect square on the left side:
(w + 3)(w + 3) = 7.8

Calculate the square root of the right side: 2.792848009

Break this problem into two subproblems by setting 
(w + 3) equal to 2.792848009 and -2.792848009.

Subproblem 1
w + 3 = 2.792848009

Simplifying
w + 3 = 2.792848009

Reorder the terms:
3 + w = 2.792848009

Solving
3 + w = 2.792848009

Solving for variable 'w'.

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

Add '-3' to each side of the equation.
3 + -3 + w = 2.792848009 + -3

Combine like terms: 3 + -3 = 0
0 + w = 2.792848009 + -3
w = 2.792848009 + -3

Combine like terms: 2.792848009 + -3 = -0.207151991
w = -0.207151991

Simplifying
w = -0.207151991

Subproblem 2
w + 3 = -2.792848009

Simplifying
w + 3 = -2.792848009

Reorder the terms:
3 + w = -2.792848009

Solving
3 + w = -2.792848009

Solving for variable 'w'.

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

Add '-3' to each side of the equation.
3 + -3 + w = -2.792848009 + -3

Combine like terms: 3 + -3 = 0
0 + w = -2.792848009 + -3
w = -2.792848009 + -3

Combine like terms: -2.792848009 + -3 = -5.792848009
w = -5.792848009

Simplifying
w = -5.792848009

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.207151991, -5.792848009}