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 = 1.585876621
x = 1.585876621

Simplifying
x = 1.585876621

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 = -9.728733765
x = -9.728733765

Simplifying
x = -9.728733765

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