4x^2+346x-2640=0

Solution for 4x^2+346x-2640=0 equation:

Simplifying
4x2 + 346x + -2640 = 0

Reorder the terms:
-2640 + 346x + 4x2 = 0

Solving
-2640 + 346x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1320 + 173x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1320 + 173x + 2x2)' equal to zero and attempt to solve:

Simplifying
-1320 + 173x + 2x2 = 0

Solving
-1320 + 173x + 2x2 = 0

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

Divide each side by '2'.
-660 + 86.5x + x2 = 0

Move the constant term to the right:

Add '660' to each side of the equation.
-660 + 86.5x + 660 + x2 = 0 + 660

Reorder the terms:
-660 + 660 + 86.5x + x2 = 0 + 660

Combine like terms: -660 + 660 = 0
0 + 86.5x + x2 = 0 + 660
86.5x + x2 = 0 + 660

Combine like terms: 0 + 660 = 660
86.5x + x2 = 660

The x term is 86.5x.  Take half its coefficient (43.25).
Square it (1870.5625) and add it to both sides.

Add '1870.5625' to each side of the equation.
86.5x + 1870.5625 + x2 = 660 + 1870.5625

Reorder the terms:
1870.5625 + 86.5x + x2 = 660 + 1870.5625

Combine like terms: 660 + 1870.5625 = 2530.5625
1870.5625 + 86.5x + x2 = 2530.5625

Factor a perfect square on the left side:
(x + 43.25)(x + 43.25) = 2530.5625

Calculate the square root of the right side: 50.3046966

Break this problem into two subproblems by setting 
(x + 43.25) equal to 50.3046966 and -50.3046966.

Subproblem 1
x + 43.25 = 50.3046966

Simplifying
x + 43.25 = 50.3046966

Reorder the terms:
43.25 + x = 50.3046966

Solving
43.25 + x = 50.3046966

Solving for variable 'x'.

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

Add '-43.25' to each side of the equation.
43.25 + -43.25 + x = 50.3046966 + -43.25

Combine like terms: 43.25 + -43.25 = 0.00
0.00 + x = 50.3046966 + -43.25
x = 50.3046966 + -43.25

Combine like terms: 50.3046966 + -43.25 = 7.0546966
x = 7.0546966

Simplifying
x = 7.0546966

Subproblem 2
x + 43.25 = -50.3046966

Simplifying
x + 43.25 = -50.3046966

Reorder the terms:
43.25 + x = -50.3046966

Solving
43.25 + x = -50.3046966

Solving for variable 'x'.

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

Add '-43.25' to each side of the equation.
43.25 + -43.25 + x = -50.3046966 + -43.25

Combine like terms: 43.25 + -43.25 = 0.00
0.00 + x = -50.3046966 + -43.25
x = -50.3046966 + -43.25

Combine like terms: -50.3046966 + -43.25 = -93.5546966
x = -93.5546966

Simplifying
x = -93.5546966

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.0546966, -93.5546966}
Solution
x = {7.0546966, -93.5546966}