704x^2-30x-20640=0

Solution for 704x^2-30x-20640=0 equation:

Simplifying
704x2 + -30x + -20640 = 0

Reorder the terms:
-20640 + -30x + 704x2 = 0

Solving
-20640 + -30x + 704x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10320 + -15x + 352x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10320 + -15x + 352x2)' equal to zero and attempt to solve:

Simplifying
-10320 + -15x + 352x2 = 0

Solving
-10320 + -15x + 352x2 = 0

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

Divide each side by '352'.
-29.31818182 + -0.04261363636x + x2 = 0

Move the constant term to the right:

Add '29.31818182' to each side of the equation.
-29.31818182 + -0.04261363636x + 29.31818182 + x2 = 0 + 29.31818182

Reorder the terms:
-29.31818182 + 29.31818182 + -0.04261363636x + x2 = 0 + 29.31818182

Combine like terms: -29.31818182 + 29.31818182 = 0.00000000
0.00000000 + -0.04261363636x + x2 = 0 + 29.31818182
-0.04261363636x + x2 = 0 + 29.31818182

Combine like terms: 0 + 29.31818182 = 29.31818182
-0.04261363636x + x2 = 29.31818182

The x term is -0.04261363636x.  Take half its coefficient (-0.02130681818).
Square it (0.0004539805010) and add it to both sides.

Add '0.0004539805010' to each side of the equation.
-0.04261363636x + 0.0004539805010 + x2 = 29.31818182 + 0.0004539805010

Reorder the terms:
0.0004539805010 + -0.04261363636x + x2 = 29.31818182 + 0.0004539805010

Combine like terms: 29.31818182 + 0.0004539805010 = 29.318635800501
0.0004539805010 + -0.04261363636x + x2 = 29.318635800501

Factor a perfect square on the left side:
(x + -0.02130681818)(x + -0.02130681818) = 29.318635800501

Calculate the square root of the right side: 5.414668577

Break this problem into two subproblems by setting 
(x + -0.02130681818) equal to 5.414668577 and -5.414668577.

Subproblem 1
x + -0.02130681818 = 5.414668577

Simplifying
x + -0.02130681818 = 5.414668577

Reorder the terms:
-0.02130681818 + x = 5.414668577

Solving
-0.02130681818 + x = 5.414668577

Solving for variable 'x'.

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

Add '0.02130681818' to each side of the equation.
-0.02130681818 + 0.02130681818 + x = 5.414668577 + 0.02130681818

Combine like terms: -0.02130681818 + 0.02130681818 = 0.00000000000
0.00000000000 + x = 5.414668577 + 0.02130681818
x = 5.414668577 + 0.02130681818

Combine like terms: 5.414668577 + 0.02130681818 = 5.43597539518
x = 5.43597539518

Simplifying
x = 5.43597539518

Subproblem 2
x + -0.02130681818 = -5.414668577

Simplifying
x + -0.02130681818 = -5.414668577

Reorder the terms:
-0.02130681818 + x = -5.414668577

Solving
-0.02130681818 + x = -5.414668577

Solving for variable 'x'.

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

Add '0.02130681818' to each side of the equation.
-0.02130681818 + 0.02130681818 + x = -5.414668577 + 0.02130681818

Combine like terms: -0.02130681818 + 0.02130681818 = 0.00000000000
0.00000000000 + x = -5.414668577 + 0.02130681818
x = -5.414668577 + 0.02130681818

Combine like terms: -5.414668577 + 0.02130681818 = -5.39336175882
x = -5.39336175882

Simplifying
x = -5.39336175882

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.43597539518, -5.39336175882}
Solution
x = {5.43597539518, -5.39336175882}