3s^2+19s+18=0

Solution for 3s^2+19s+18=0 equation:

Simplifying
3s2 + 19s + 18 = 0

Reorder the terms:
18 + 19s + 3s2 = 0

Solving
18 + 19s + 3s2 = 0

Solving for variable 's'.

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

Divide each side by '3'.
6 + 6.333333333s + s2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 6.333333333s + -6 + s2 = 0 + -6

Reorder the terms:
6 + -6 + 6.333333333s + s2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 6.333333333s + s2 = 0 + -6
6.333333333s + s2 = 0 + -6

Combine like terms: 0 + -6 = -6
6.333333333s + s2 = -6

The s term is 6.333333333s.  Take half its coefficient (3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
6.333333333s + 10.02777778 + s2 = -6 + 10.02777778

Reorder the terms:
10.02777778 + 6.333333333s + s2 = -6 + 10.02777778

Combine like terms: -6 + 10.02777778 = 4.02777778
10.02777778 + 6.333333333s + s2 = 4.02777778

Factor a perfect square on the left side:
(s + 3.166666667)(s + 3.166666667) = 4.02777778

Calculate the square root of the right side: 2.00693243

Break this problem into two subproblems by setting 
(s + 3.166666667) equal to 2.00693243 and -2.00693243.

Subproblem 1
s + 3.166666667 = 2.00693243

Simplifying
s + 3.166666667 = 2.00693243

Reorder the terms:
3.166666667 + s = 2.00693243

Solving
3.166666667 + s = 2.00693243

Solving for variable 's'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + s = 2.00693243 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + s = 2.00693243 + -3.166666667
s = 2.00693243 + -3.166666667

Combine like terms: 2.00693243 + -3.166666667 = -1.159734237
s = -1.159734237

Simplifying
s = -1.159734237

Subproblem 2
s + 3.166666667 = -2.00693243

Simplifying
s + 3.166666667 = -2.00693243

Reorder the terms:
3.166666667 + s = -2.00693243

Solving
3.166666667 + s = -2.00693243

Solving for variable 's'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + s = -2.00693243 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + s = -2.00693243 + -3.166666667
s = -2.00693243 + -3.166666667

Combine like terms: -2.00693243 + -3.166666667 = -5.173599097
s = -5.173599097

Simplifying
s = -5.173599097

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-1.159734237, -5.173599097}