24x^2+780x-5000=0

Solution for 24x^2+780x-5000=0 equation:

Simplifying
24x2 + 780x + -5000 = 0

Reorder the terms:
-5000 + 780x + 24x2 = 0

Solving
-5000 + 780x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1250 + 195x + 6x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1250 + 195x + 6x2)' equal to zero and attempt to solve:

Simplifying
-1250 + 195x + 6x2 = 0

Solving
-1250 + 195x + 6x2 = 0

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

Divide each side by '6'.
-208.3333333 + 32.5x + x2 = 0

Move the constant term to the right:

Add '208.3333333' to each side of the equation.
-208.3333333 + 32.5x + 208.3333333 + x2 = 0 + 208.3333333

Reorder the terms:
-208.3333333 + 208.3333333 + 32.5x + x2 = 0 + 208.3333333

Combine like terms: -208.3333333 + 208.3333333 = 0.0000000
0.0000000 + 32.5x + x2 = 0 + 208.3333333
32.5x + x2 = 0 + 208.3333333

Combine like terms: 0 + 208.3333333 = 208.3333333
32.5x + x2 = 208.3333333

The x term is 32.5x.  Take half its coefficient (16.25).
Square it (264.0625) and add it to both sides.

Add '264.0625' to each side of the equation.
32.5x + 264.0625 + x2 = 208.3333333 + 264.0625

Reorder the terms:
264.0625 + 32.5x + x2 = 208.3333333 + 264.0625

Combine like terms: 208.3333333 + 264.0625 = 472.3958333
264.0625 + 32.5x + x2 = 472.3958333

Factor a perfect square on the left side:
(x + 16.25)(x + 16.25) = 472.3958333

Calculate the square root of the right side: 21.734668925

Break this problem into two subproblems by setting 
(x + 16.25) equal to 21.734668925 and -21.734668925.

Subproblem 1
x + 16.25 = 21.734668925

Simplifying
x + 16.25 = 21.734668925

Reorder the terms:
16.25 + x = 21.734668925

Solving
16.25 + x = 21.734668925

Solving for variable 'x'.

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

Add '-16.25' to each side of the equation.
16.25 + -16.25 + x = 21.734668925 + -16.25

Combine like terms: 16.25 + -16.25 = 0.00
0.00 + x = 21.734668925 + -16.25
x = 21.734668925 + -16.25

Combine like terms: 21.734668925 + -16.25 = 5.484668925
x = 5.484668925

Simplifying
x = 5.484668925

Subproblem 2
x + 16.25 = -21.734668925

Simplifying
x + 16.25 = -21.734668925

Reorder the terms:
16.25 + x = -21.734668925

Solving
16.25 + x = -21.734668925

Solving for variable 'x'.

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

Add '-16.25' to each side of the equation.
16.25 + -16.25 + x = -21.734668925 + -16.25

Combine like terms: 16.25 + -16.25 = 0.00
0.00 + x = -21.734668925 + -16.25
x = -21.734668925 + -16.25

Combine like terms: -21.734668925 + -16.25 = -37.984668925
x = -37.984668925

Simplifying
x = -37.984668925

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.484668925, -37.984668925}
Solution
x = {5.484668925, -37.984668925}