8.2s(s+4)=6.7s+5.2

Solution for 8.2s(s+4)=6.7s+5.2 equation:

Simplifying
8.2s(s + 4) = 6.7s + 5.2

Reorder the terms:
8.2s(4 + s) = 6.7s + 5.2
(4 * 8.2s + s * 8.2s) = 6.7s + 5.2
(32.8s + 8.2s2) = 6.7s + 5.2

Reorder the terms:
32.8s + 8.2s2 = 5.2 + 6.7s

Solving
32.8s + 8.2s2 = 5.2 + 6.7s

Solving for variable 's'.

Reorder the terms:
-5.2 + 32.8s + -6.7s + 8.2s2 = 5.2 + 6.7s + -5.2 + -6.7s

Combine like terms: 32.8s + -6.7s = 26.1s
-5.2 + 26.1s + 8.2s2 = 5.2 + 6.7s + -5.2 + -6.7s

Reorder the terms:
-5.2 + 26.1s + 8.2s2 = 5.2 + -5.2 + 6.7s + -6.7s

Combine like terms: 5.2 + -5.2 = 0.0
-5.2 + 26.1s + 8.2s2 = 0.0 + 6.7s + -6.7s
-5.2 + 26.1s + 8.2s2 = 6.7s + -6.7s

Combine like terms: 6.7s + -6.7s = 0.0
-5.2 + 26.1s + 8.2s2 = 0.0

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

Divide each side by '8.2'.
-0.6341463415 + 3.182926829s + s2 = 0

Move the constant term to the right:

Add '0.6341463415' to each side of the equation.
-0.6341463415 + 3.182926829s + 0.6341463415 + s2 = 0 + 0.6341463415

Reorder the terms:
-0.6341463415 + 0.6341463415 + 3.182926829s + s2 = 0 + 0.6341463415

Combine like terms: -0.6341463415 + 0.6341463415 = 0.0000000000
0.0000000000 + 3.182926829s + s2 = 0 + 0.6341463415
3.182926829s + s2 = 0 + 0.6341463415

Combine like terms: 0 + 0.6341463415 = 0.6341463415
3.182926829s + s2 = 0.6341463415

The s term is 3.182926829s.  Take half its coefficient (1.591463415).
Square it (2.532755801) and add it to both sides.

Add '2.532755801' to each side of the equation.
3.182926829s + 2.532755801 + s2 = 0.6341463415 + 2.532755801

Reorder the terms:
2.532755801 + 3.182926829s + s2 = 0.6341463415 + 2.532755801

Combine like terms: 0.6341463415 + 2.532755801 = 3.1669021425
2.532755801 + 3.182926829s + s2 = 3.1669021425

Factor a perfect square on the left side:
(s + 1.591463415)(s + 1.591463415) = 3.1669021425

Calculate the square root of the right side: 1.779579204

Break this problem into two subproblems by setting 
(s + 1.591463415) equal to 1.779579204 and -1.779579204.

Subproblem 1
s + 1.591463415 = 1.779579204

Simplifying
s + 1.591463415 = 1.779579204

Reorder the terms:
1.591463415 + s = 1.779579204

Solving
1.591463415 + s = 1.779579204

Solving for variable 's'.

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

Add '-1.591463415' to each side of the equation.
1.591463415 + -1.591463415 + s = 1.779579204 + -1.591463415

Combine like terms: 1.591463415 + -1.591463415 = 0.000000000
0.000000000 + s = 1.779579204 + -1.591463415
s = 1.779579204 + -1.591463415

Combine like terms: 1.779579204 + -1.591463415 = 0.188115789
s = 0.188115789

Simplifying
s = 0.188115789

Subproblem 2
s + 1.591463415 = -1.779579204

Simplifying
s + 1.591463415 = -1.779579204

Reorder the terms:
1.591463415 + s = -1.779579204

Solving
1.591463415 + s = -1.779579204

Solving for variable 's'.

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

Add '-1.591463415' to each side of the equation.
1.591463415 + -1.591463415 + s = -1.779579204 + -1.591463415

Combine like terms: 1.591463415 + -1.591463415 = 0.000000000
0.000000000 + s = -1.779579204 + -1.591463415
s = -1.779579204 + -1.591463415

Combine like terms: -1.779579204 + -1.591463415 = -3.371042619
s = -3.371042619

Simplifying
s = -3.371042619

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.188115789, -3.371042619}