3.25x^2+6x-96=0

Solution for 3.25x^2+6x-96=0 equation:

Simplifying
3.25x2 + 6x + -96 = 0

Reorder the terms:
-96 + 6x + 3.25x2 = 0

Solving
-96 + 6x + 3.25x2 = 0

Solving for variable 'x'.

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

Divide each side by '3.25'.
-29.53846154 + 1.846153846x + x2 = 0

Move the constant term to the right:

Add '29.53846154' to each side of the equation.
-29.53846154 + 1.846153846x + 29.53846154 + x2 = 0 + 29.53846154

Reorder the terms:
-29.53846154 + 29.53846154 + 1.846153846x + x2 = 0 + 29.53846154

Combine like terms: -29.53846154 + 29.53846154 = 0.00000000
0.00000000 + 1.846153846x + x2 = 0 + 29.53846154
1.846153846x + x2 = 0 + 29.53846154

Combine like terms: 0 + 29.53846154 = 29.53846154
1.846153846x + x2 = 29.53846154

The x term is 1.846153846x.  Take half its coefficient (0.923076923).
Square it (0.8520710058) and add it to both sides.

Add '0.8520710058' to each side of the equation.
1.846153846x + 0.8520710058 + x2 = 29.53846154 + 0.8520710058

Reorder the terms:
0.8520710058 + 1.846153846x + x2 = 29.53846154 + 0.8520710058

Combine like terms: 29.53846154 + 0.8520710058 = 30.3905325458
0.8520710058 + 1.846153846x + x2 = 30.3905325458

Factor a perfect square on the left side:
(x + 0.923076923)(x + 0.923076923) = 30.3905325458

Calculate the square root of the right side: 5.512760882

Break this problem into two subproblems by setting 
(x + 0.923076923) equal to 5.512760882 and -5.512760882.

Subproblem 1
x + 0.923076923 = 5.512760882

Simplifying
x + 0.923076923 = 5.512760882

Reorder the terms:
0.923076923 + x = 5.512760882

Solving
0.923076923 + x = 5.512760882

Solving for variable 'x'.

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

Add '-0.923076923' to each side of the equation.
0.923076923 + -0.923076923 + x = 5.512760882 + -0.923076923

Combine like terms: 0.923076923 + -0.923076923 = 0.000000000
0.000000000 + x = 5.512760882 + -0.923076923
x = 5.512760882 + -0.923076923

Combine like terms: 5.512760882 + -0.923076923 = 4.589683959
x = 4.589683959

Simplifying
x = 4.589683959

Subproblem 2
x + 0.923076923 = -5.512760882

Simplifying
x + 0.923076923 = -5.512760882

Reorder the terms:
0.923076923 + x = -5.512760882

Solving
0.923076923 + x = -5.512760882

Solving for variable 'x'.

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

Add '-0.923076923' to each side of the equation.
0.923076923 + -0.923076923 + x = -5.512760882 + -0.923076923

Combine like terms: 0.923076923 + -0.923076923 = 0.000000000
0.000000000 + x = -5.512760882 + -0.923076923
x = -5.512760882 + -0.923076923

Combine like terms: -5.512760882 + -0.923076923 = -6.435837805
x = -6.435837805

Simplifying
x = -6.435837805

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.589683959, -6.435837805}