3.9x^2+6.8x-12=0

Solution for 3.9x^2+6.8x-12=0 equation:

Simplifying
3.9x2 + 6.8x + -12 = 0

Reorder the terms:
-12 + 6.8x + 3.9x2 = 0

Solving
-12 + 6.8x + 3.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '3.9'.
-3.076923077 + 1.743589744x + x2 = 0

Move the constant term to the right:

Add '3.076923077' to each side of the equation.
-3.076923077 + 1.743589744x + 3.076923077 + x2 = 0 + 3.076923077

Reorder the terms:
-3.076923077 + 3.076923077 + 1.743589744x + x2 = 0 + 3.076923077

Combine like terms: -3.076923077 + 3.076923077 = 0.000000000
0.000000000 + 1.743589744x + x2 = 0 + 3.076923077
1.743589744x + x2 = 0 + 3.076923077

Combine like terms: 0 + 3.076923077 = 3.076923077
1.743589744x + x2 = 3.076923077

The x term is 1.743589744x.  Take half its coefficient (0.871794872).
Square it (0.7600262988) and add it to both sides.

Add '0.7600262988' to each side of the equation.
1.743589744x + 0.7600262988 + x2 = 3.076923077 + 0.7600262988

Reorder the terms:
0.7600262988 + 1.743589744x + x2 = 3.076923077 + 0.7600262988

Combine like terms: 3.076923077 + 0.7600262988 = 3.8369493758
0.7600262988 + 1.743589744x + x2 = 3.8369493758

Factor a perfect square on the left side:
(x + 0.871794872)(x + 0.871794872) = 3.8369493758

Calculate the square root of the right side: 1.958813257

Break this problem into two subproblems by setting 
(x + 0.871794872) equal to 1.958813257 and -1.958813257.

Subproblem 1
x + 0.871794872 = 1.958813257

Simplifying
x + 0.871794872 = 1.958813257

Reorder the terms:
0.871794872 + x = 1.958813257

Solving
0.871794872 + x = 1.958813257

Solving for variable 'x'.

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

Add '-0.871794872' to each side of the equation.
0.871794872 + -0.871794872 + x = 1.958813257 + -0.871794872

Combine like terms: 0.871794872 + -0.871794872 = 0.000000000
0.000000000 + x = 1.958813257 + -0.871794872
x = 1.958813257 + -0.871794872

Combine like terms: 1.958813257 + -0.871794872 = 1.087018385
x = 1.087018385

Simplifying
x = 1.087018385

Subproblem 2
x + 0.871794872 = -1.958813257

Simplifying
x + 0.871794872 = -1.958813257

Reorder the terms:
0.871794872 + x = -1.958813257

Solving
0.871794872 + x = -1.958813257

Solving for variable 'x'.

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

Add '-0.871794872' to each side of the equation.
0.871794872 + -0.871794872 + x = -1.958813257 + -0.871794872

Combine like terms: 0.871794872 + -0.871794872 = 0.000000000
0.000000000 + x = -1.958813257 + -0.871794872
x = -1.958813257 + -0.871794872

Combine like terms: -1.958813257 + -0.871794872 = -2.830608129
x = -2.830608129

Simplifying
x = -2.830608129

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.087018385, -2.830608129}