6.84x^2+1140x-37000=0

Solution for 6.84x^2+1140x-37000=0 equation:

Simplifying
6.84x2 + 1140x + -37000 = 0

Reorder the terms:
-37000 + 1140x + 6.84x2 = 0

Solving
-37000 + 1140x + 6.84x2 = 0

Solving for variable 'x'.

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

Divide each side by '6.84'.
-5409.356725 + 166.6666667x + x2 = 0

Move the constant term to the right:

Add '5409.356725' to each side of the equation.
-5409.356725 + 166.6666667x + 5409.356725 + x2 = 0 + 5409.356725

Reorder the terms:
-5409.356725 + 5409.356725 + 166.6666667x + x2 = 0 + 5409.356725

Combine like terms: -5409.356725 + 5409.356725 = 0.000000
0.000000 + 166.6666667x + x2 = 0 + 5409.356725
166.6666667x + x2 = 0 + 5409.356725

Combine like terms: 0 + 5409.356725 = 5409.356725
166.6666667x + x2 = 5409.356725

The x term is 166.6666667x.  Take half its coefficient (83.33333335).
Square it (6944.444447) and add it to both sides.

Add '6944.444447' to each side of the equation.
166.6666667x + 6944.444447 + x2 = 5409.356725 + 6944.444447

Reorder the terms:
6944.444447 + 166.6666667x + x2 = 5409.356725 + 6944.444447

Combine like terms: 5409.356725 + 6944.444447 = 12353.801172
6944.444447 + 166.6666667x + x2 = 12353.801172

Factor a perfect square on the left side:
(x + 83.33333335)(x + 83.33333335) = 12353.801172

Calculate the square root of the right side: 111.14765482

Break this problem into two subproblems by setting 
(x + 83.33333335) equal to 111.14765482 and -111.14765482.

Subproblem 1
x + 83.33333335 = 111.14765482

Simplifying
x + 83.33333335 = 111.14765482

Reorder the terms:
83.33333335 + x = 111.14765482

Solving
83.33333335 + x = 111.14765482

Solving for variable 'x'.

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

Add '-83.33333335' to each side of the equation.
83.33333335 + -83.33333335 + x = 111.14765482 + -83.33333335

Combine like terms: 83.33333335 + -83.33333335 = 0.00000000
0.00000000 + x = 111.14765482 + -83.33333335
x = 111.14765482 + -83.33333335

Combine like terms: 111.14765482 + -83.33333335 = 27.81432147
x = 27.81432147

Simplifying
x = 27.81432147

Subproblem 2
x + 83.33333335 = -111.14765482

Simplifying
x + 83.33333335 = -111.14765482

Reorder the terms:
83.33333335 + x = -111.14765482

Solving
83.33333335 + x = -111.14765482

Solving for variable 'x'.

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

Add '-83.33333335' to each side of the equation.
83.33333335 + -83.33333335 + x = -111.14765482 + -83.33333335

Combine like terms: 83.33333335 + -83.33333335 = 0.00000000
0.00000000 + x = -111.14765482 + -83.33333335
x = -111.14765482 + -83.33333335

Combine like terms: -111.14765482 + -83.33333335 = -194.48098817
x = -194.48098817

Simplifying
x = -194.48098817

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.81432147, -194.48098817}