3.2x^2-16.8x-16.8=0

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Solution for 3.2x^2-16.8x-16.8=0 equation: 


Simplifying
3.2x2 + -16.8x + -16.8 = 0

Reorder the terms:
-16.8 + -16.8x + 3.2x2 = 0

Solving
-16.8 + -16.8x + 3.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '3.2'.
-5.25 + -5.25x + x2 = 0

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + -5.25x + 5.25 + x2 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + -5.25x + x2 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + -5.25x + x2 = 0 + 5.25
-5.25x + x2 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
-5.25x + x2 = 5.25

The x term is -5.25x.  Take half its coefficient (-2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
-5.25x + 6.890625 + x2 = 5.25 + 6.890625

Reorder the terms:
6.890625 + -5.25x + x2 = 5.25 + 6.890625

Combine like terms: 5.25 + 6.890625 = 12.140625
6.890625 + -5.25x + x2 = 12.140625

Factor a perfect square on the left side:
(x + -2.625)(x + -2.625) = 12.140625

Calculate the square root of the right side: 3.484339966

Break this problem into two subproblems by setting 
(x + -2.625) equal to 3.484339966 and -3.484339966.


Subproblem 1
x + -2.625 = 3.484339966

Simplifying
x + -2.625 = 3.484339966

Reorder the terms:
-2.625 + x = 3.484339966

Solving
-2.625 + x = 3.484339966

Solving for variable 'x'.

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

Add '2.625' to each side of the equation.
-2.625 + 2.625 + x = 3.484339966 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + x = 3.484339966 + 2.625
x = 3.484339966 + 2.625

Combine like terms: 3.484339966 + 2.625 = 6.109339966
x = 6.109339966

Simplifying
x = 6.109339966


Subproblem 2
x + -2.625 = -3.484339966

Simplifying
x + -2.625 = -3.484339966

Reorder the terms:
-2.625 + x = -3.484339966

Solving
-2.625 + x = -3.484339966

Solving for variable 'x'.

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

Add '2.625' to each side of the equation.
-2.625 + 2.625 + x = -3.484339966 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + x = -3.484339966 + 2.625
x = -3.484339966 + 2.625

Combine like terms: -3.484339966 + 2.625 = -0.859339966
x = -0.859339966

Simplifying
x = -0.859339966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.109339966, -0.859339966}

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