-3s^2+28s-48=0

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Solution for -3s^2+28s-48=0 equation: 


Simplifying
-3s2 + 28s + -48 = 0

Reorder the terms:
-48 + 28s + -3s2 = 0

Solving
-48 + 28s + -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'.
16 + -9.333333333s + s2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -9.333333333s + -16 + s2 = 0 + -16

Reorder the terms:
16 + -16 + -9.333333333s + s2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -9.333333333s + s2 = 0 + -16
-9.333333333s + s2 = 0 + -16

Combine like terms: 0 + -16 = -16
-9.333333333s + s2 = -16

The s term is -9.333333333s.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333s + 21.77777778 + s2 = -16 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333s + s2 = -16 + 21.77777778

Combine like terms: -16 + 21.77777778 = 5.77777778
21.77777778 + -9.333333333s + s2 = 5.77777778

Factor a perfect square on the left side:
(s + -4.666666667)(s + -4.666666667) = 5.77777778

Calculate the square root of the right side: 2.403700851

Break this problem into two subproblems by setting 
(s + -4.666666667) equal to 2.403700851 and -2.403700851.


Subproblem 1
s + -4.666666667 = 2.403700851

Simplifying
s + -4.666666667 = 2.403700851

Reorder the terms:
-4.666666667 + s = 2.403700851

Solving
-4.666666667 + s = 2.403700851

Solving for variable 's'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + s = 2.403700851 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + s = 2.403700851 + 4.666666667
s = 2.403700851 + 4.666666667

Combine like terms: 2.403700851 + 4.666666667 = 7.070367518
s = 7.070367518

Simplifying
s = 7.070367518


Subproblem 2
s + -4.666666667 = -2.403700851

Simplifying
s + -4.666666667 = -2.403700851

Reorder the terms:
-4.666666667 + s = -2.403700851

Solving
-4.666666667 + s = -2.403700851

Solving for variable 's'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + s = -2.403700851 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + s = -2.403700851 + 4.666666667
s = -2.403700851 + 4.666666667

Combine like terms: -2.403700851 + 4.666666667 = 2.262965816
s = 2.262965816

Simplifying
s = 2.262965816


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {7.070367518, 2.262965816}

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