7x^2-12x-84=0

Solution for 7x^2-12x-84=0 equation:

Simplifying
7x2 + -12x + -84 = 0

Reorder the terms:
-84 + -12x + 7x2 = 0

Solving
-84 + -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'.
-12 + -1.714285714x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -1.714285714x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -1.714285714x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1.714285714x + x2 = 0 + 12
-1.714285714x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-1.714285714x + x2 = 12

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 = 12 + 0.7346938773

Reorder the terms:
0.7346938773 + -1.714285714x + x2 = 12 + 0.7346938773

Combine like terms: 12 + 0.7346938773 = 12.7346938773
0.7346938773 + -1.714285714x + x2 = 12.7346938773

Factor a perfect square on the left side:
(x + -0.857142857)(x + -0.857142857) = 12.7346938773

Calculate the square root of the right side: 3.568570285

Break this problem into two subproblems by setting 
(x + -0.857142857) equal to 3.568570285 and -3.568570285.

Subproblem 1
x + -0.857142857 = 3.568570285

Simplifying
x + -0.857142857 = 3.568570285

Reorder the terms:
-0.857142857 + x = 3.568570285

Solving
-0.857142857 + x = 3.568570285

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 = 3.568570285 + 0.857142857

Combine like terms: -0.857142857 + 0.857142857 = 0.000000000
0.000000000 + x = 3.568570285 + 0.857142857
x = 3.568570285 + 0.857142857

Combine like terms: 3.568570285 + 0.857142857 = 4.425713142
x = 4.425713142

Simplifying
x = 4.425713142

Subproblem 2
x + -0.857142857 = -3.568570285

Simplifying
x + -0.857142857 = -3.568570285

Reorder the terms:
-0.857142857 + x = -3.568570285

Solving
-0.857142857 + x = -3.568570285

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 = -3.568570285 + 0.857142857

Combine like terms: -0.857142857 + 0.857142857 = 0.000000000
0.000000000 + x = -3.568570285 + 0.857142857
x = -3.568570285 + 0.857142857

Combine like terms: -3.568570285 + 0.857142857 = -2.711427428
x = -2.711427428

Simplifying
x = -2.711427428

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.425713142, -2.711427428}