7x^2-57x-108=0

Solution for 7x^2-57x-108=0 equation:

Simplifying
7x2 + -57x + -108 = 0

Reorder the terms:
-108 + -57x + 7x2 = 0

Solving
-108 + -57x + 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'.
-15.42857143 + -8.142857143x + x2 = 0

Move the constant term to the right:

Add '15.42857143' to each side of the equation.
-15.42857143 + -8.142857143x + 15.42857143 + x2 = 0 + 15.42857143

Reorder the terms:
-15.42857143 + 15.42857143 + -8.142857143x + x2 = 0 + 15.42857143

Combine like terms: -15.42857143 + 15.42857143 = 0.00000000
0.00000000 + -8.142857143x + x2 = 0 + 15.42857143
-8.142857143x + x2 = 0 + 15.42857143

Combine like terms: 0 + 15.42857143 = 15.42857143
-8.142857143x + x2 = 15.42857143

The x term is -8.142857143x.  Take half its coefficient (-4.071428572).
Square it (16.57653062) and add it to both sides.

Add '16.57653062' to each side of the equation.
-8.142857143x + 16.57653062 + x2 = 15.42857143 + 16.57653062

Reorder the terms:
16.57653062 + -8.142857143x + x2 = 15.42857143 + 16.57653062

Combine like terms: 15.42857143 + 16.57653062 = 32.00510205
16.57653062 + -8.142857143x + x2 = 32.00510205

Factor a perfect square on the left side:
(x + -4.071428572)(x + -4.071428572) = 32.00510205

Calculate the square root of the right side: 5.657305193

Break this problem into two subproblems by setting 
(x + -4.071428572) equal to 5.657305193 and -5.657305193.

Subproblem 1
x + -4.071428572 = 5.657305193

Simplifying
x + -4.071428572 = 5.657305193

Reorder the terms:
-4.071428572 + x = 5.657305193

Solving
-4.071428572 + x = 5.657305193

Solving for variable 'x'.

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

Add '4.071428572' to each side of the equation.
-4.071428572 + 4.071428572 + x = 5.657305193 + 4.071428572

Combine like terms: -4.071428572 + 4.071428572 = 0.000000000
0.000000000 + x = 5.657305193 + 4.071428572
x = 5.657305193 + 4.071428572

Combine like terms: 5.657305193 + 4.071428572 = 9.728733765
x = 9.728733765

Simplifying
x = 9.728733765

Subproblem 2
x + -4.071428572 = -5.657305193

Simplifying
x + -4.071428572 = -5.657305193

Reorder the terms:
-4.071428572 + x = -5.657305193

Solving
-4.071428572 + x = -5.657305193

Solving for variable 'x'.

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

Add '4.071428572' to each side of the equation.
-4.071428572 + 4.071428572 + x = -5.657305193 + 4.071428572

Combine like terms: -4.071428572 + 4.071428572 = 0.000000000
0.000000000 + x = -5.657305193 + 4.071428572
x = -5.657305193 + 4.071428572

Combine like terms: -5.657305193 + 4.071428572 = -1.585876621
x = -1.585876621

Simplifying
x = -1.585876621

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.728733765, -1.585876621}