7x^2+12x-1296=0

Solution for 7x^2+12x-1296=0 equation:

Simplifying
7x2 + 12x + -1296 = 0

Reorder the terms:
-1296 + 12x + 7x2 = 0

Solving
-1296 + 12x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-185.1428571 + 1.714285714x + x2 = 0

Move the constant term to the right:

Add '185.1428571' to each side of the equation.
-185.1428571 + 1.714285714x + 185.1428571 + x2 = 0 + 185.1428571

Reorder the terms:
-185.1428571 + 185.1428571 + 1.714285714x + x2 = 0 + 185.1428571

Combine like terms: -185.1428571 + 185.1428571 = 0.0000000
0.0000000 + 1.714285714x + x2 = 0 + 185.1428571
1.714285714x + x2 = 0 + 185.1428571

Combine like terms: 0 + 185.1428571 = 185.1428571
1.714285714x + x2 = 185.1428571

The x term is 1.714285714x.  Take half its coefficient (0.857142857).
Square it (0.7346938773) and add it to both sides.

Add '0.7346938773' to each side of the equation.
1.714285714x + 0.7346938773 + x2 = 185.1428571 + 0.7346938773

Reorder the terms:
0.7346938773 + 1.714285714x + x2 = 185.1428571 + 0.7346938773

Combine like terms: 185.1428571 + 0.7346938773 = 185.8775509773
0.7346938773 + 1.714285714x + x2 = 185.8775509773

Factor a perfect square on the left side:
(x + 0.857142857)(x + 0.857142857) = 185.8775509773

Calculate the square root of the right side: 13.633691759

Break this problem into two subproblems by setting 
(x + 0.857142857) equal to 13.633691759 and -13.633691759.

Subproblem 1
x + 0.857142857 = 13.633691759

Simplifying
x + 0.857142857 = 13.633691759

Reorder the terms:
0.857142857 + x = 13.633691759

Solving
0.857142857 + x = 13.633691759

Solving for variable 'x'.

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

Add '-0.857142857' to each side of the equation.
0.857142857 + -0.857142857 + x = 13.633691759 + -0.857142857

Combine like terms: 0.857142857 + -0.857142857 = 0.000000000
0.000000000 + x = 13.633691759 + -0.857142857
x = 13.633691759 + -0.857142857

Combine like terms: 13.633691759 + -0.857142857 = 12.776548902
x = 12.776548902

Simplifying
x = 12.776548902

Subproblem 2
x + 0.857142857 = -13.633691759

Simplifying
x + 0.857142857 = -13.633691759

Reorder the terms:
0.857142857 + x = -13.633691759

Solving
0.857142857 + x = -13.633691759

Solving for variable 'x'.

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

Add '-0.857142857' to each side of the equation.
0.857142857 + -0.857142857 + x = -13.633691759 + -0.857142857

Combine like terms: 0.857142857 + -0.857142857 = 0.000000000
0.000000000 + x = -13.633691759 + -0.857142857
x = -13.633691759 + -0.857142857

Combine like terms: -13.633691759 + -0.857142857 = -14.490834616
x = -14.490834616

Simplifying
x = -14.490834616

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.776548902, -14.490834616}