6X^2+7X-96=0

Solution for 6X^2+7X-96=0 equation:

Simplifying
6X2 + 7X + -96 = 0

Reorder the terms:
-96 + 7X + 6X2 = 0

Solving
-96 + 7X + 6X2 = 0

Solving for variable 'X'.

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

Divide each side by '6'.
-16 + 1.166666667X + X2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 1.166666667X + 16 + X2 = 0 + 16

Reorder the terms:
-16 + 16 + 1.166666667X + X2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 1.166666667X + X2 = 0 + 16
1.166666667X + X2 = 0 + 16

Combine like terms: 0 + 16 = 16
1.166666667X + X2 = 16

The X term is 1.166666667X.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667X + 0.3402777780 + X2 = 16 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667X + X2 = 16 + 0.3402777780

Combine like terms: 16 + 0.3402777780 = 16.340277778
0.3402777780 + 1.166666667X + X2 = 16.340277778

Factor a perfect square on the left side:
(X + 0.5833333335)(X + 0.5833333335) = 16.340277778

Calculate the square root of the right side: 4.042310945

Break this problem into two subproblems by setting 
(X + 0.5833333335) equal to 4.042310945 and -4.042310945.

Subproblem 1
X + 0.5833333335 = 4.042310945

Simplifying
X + 0.5833333335 = 4.042310945

Reorder the terms:
0.5833333335 + X = 4.042310945

Solving
0.5833333335 + X = 4.042310945

Solving for variable 'X'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + X = 4.042310945 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + X = 4.042310945 + -0.5833333335
X = 4.042310945 + -0.5833333335

Combine like terms: 4.042310945 + -0.5833333335 = 3.4589776115
X = 3.4589776115

Simplifying
X = 3.4589776115

Subproblem 2
X + 0.5833333335 = -4.042310945

Simplifying
X + 0.5833333335 = -4.042310945

Reorder the terms:
0.5833333335 + X = -4.042310945

Solving
0.5833333335 + X = -4.042310945

Solving for variable 'X'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + X = -4.042310945 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + X = -4.042310945 + -0.5833333335
X = -4.042310945 + -0.5833333335

Combine like terms: -4.042310945 + -0.5833333335 = -4.6256442785
X = -4.6256442785

Simplifying
X = -4.6256442785

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {3.4589776115, -4.6256442785}