400x^2+600x-8000=0

Solution for 400x^2+600x-8000=0 equation:

Simplifying
400x2 + 600x + -8000 = 0

Reorder the terms:
-8000 + 600x + 400x2 = 0

Solving
-8000 + 600x + 400x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '200'.
200(-40 + 3x + 2x2) = 0

Ignore the factor 200.
Subproblem 1
Set the factor '(-40 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
-40 + 3x + 2x2 = 0

Solving
-40 + 3x + 2x2 = 0

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

Divide each side by '2'.
-20 + 1.5x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 1.5x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 1.5x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 1.5x + x2 = 0 + 20
1.5x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
1.5x + x2 = 20

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 20 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 20 + 0.5625

Combine like terms: 20 + 0.5625 = 20.5625
0.5625 + 1.5x + x2 = 20.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 20.5625

Calculate the square root of the right side: 4.534589287

Break this problem into two subproblems by setting 
(x + 0.75) equal to 4.534589287 and -4.534589287.

Subproblem 1
x + 0.75 = 4.534589287

Simplifying
x + 0.75 = 4.534589287

Reorder the terms:
0.75 + x = 4.534589287

Solving
0.75 + x = 4.534589287

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 4.534589287 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 4.534589287 + -0.75
x = 4.534589287 + -0.75

Combine like terms: 4.534589287 + -0.75 = 3.784589287
x = 3.784589287

Simplifying
x = 3.784589287

Subproblem 2
x + 0.75 = -4.534589287

Simplifying
x + 0.75 = -4.534589287

Reorder the terms:
0.75 + x = -4.534589287

Solving
0.75 + x = -4.534589287

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -4.534589287 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -4.534589287 + -0.75
x = -4.534589287 + -0.75

Combine like terms: -4.534589287 + -0.75 = -5.284589287
x = -5.284589287

Simplifying
x = -5.284589287

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.784589287, -5.284589287}
Solution
x = {3.784589287, -5.284589287}