3x^2+3000x-24000=0

Solution for 3x^2+3000x-24000=0 equation:

Simplifying
3x2 + 3000x + -24000 = 0

Reorder the terms:
-24000 + 3000x + 3x2 = 0

Solving
-24000 + 3000x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8000 + 1000x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-8000 + 1000x + x2)' equal to zero and attempt to solve:

Simplifying
-8000 + 1000x + x2 = 0

Solving
-8000 + 1000x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8000' to each side of the equation.
-8000 + 1000x + 8000 + x2 = 0 + 8000

Reorder the terms:
-8000 + 8000 + 1000x + x2 = 0 + 8000

Combine like terms: -8000 + 8000 = 0
0 + 1000x + x2 = 0 + 8000
1000x + x2 = 0 + 8000

Combine like terms: 0 + 8000 = 8000
1000x + x2 = 8000

The x term is 1000x.  Take half its coefficient (500).
Square it (250000) and add it to both sides.

Add '250000' to each side of the equation.
1000x + 250000 + x2 = 8000 + 250000

Reorder the terms:
250000 + 1000x + x2 = 8000 + 250000

Combine like terms: 8000 + 250000 = 258000
250000 + 1000x + x2 = 258000

Factor a perfect square on the left side:
(x + 500)(x + 500) = 258000

Calculate the square root of the right side: 507.937003968

Break this problem into two subproblems by setting 
(x + 500) equal to 507.937003968 and -507.937003968.

Subproblem 1
x + 500 = 507.937003968

Simplifying
x + 500 = 507.937003968

Reorder the terms:
500 + x = 507.937003968

Solving
500 + x = 507.937003968

Solving for variable 'x'.

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

Add '-500' to each side of the equation.
500 + -500 + x = 507.937003968 + -500

Combine like terms: 500 + -500 = 0
0 + x = 507.937003968 + -500
x = 507.937003968 + -500

Combine like terms: 507.937003968 + -500 = 7.937003968
x = 7.937003968

Simplifying
x = 7.937003968

Subproblem 2
x + 500 = -507.937003968

Simplifying
x + 500 = -507.937003968

Reorder the terms:
500 + x = -507.937003968

Solving
500 + x = -507.937003968

Solving for variable 'x'.

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

Add '-500' to each side of the equation.
500 + -500 + x = -507.937003968 + -500

Combine like terms: 500 + -500 = 0
0 + x = -507.937003968 + -500
x = -507.937003968 + -500

Combine like terms: -507.937003968 + -500 = -1007.937003968
x = -1007.937003968

Simplifying
x = -1007.937003968

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.937003968, -1007.937003968}
Solution
x = {7.937003968, -1007.937003968}