2000q^2+5000q-3120=0

Solution for 2000q^2+5000q-3120=0 equation:

Simplifying
2000q2 + 5000q + -3120 = 0

Reorder the terms:
-3120 + 5000q + 2000q2 = 0

Solving
-3120 + 5000q + 2000q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '40'.
40(-78 + 125q + 50q2) = 0

Ignore the factor 40.
Subproblem 1
Set the factor '(-78 + 125q + 50q2)' equal to zero and attempt to solve:

Simplifying
-78 + 125q + 50q2 = 0

Solving
-78 + 125q + 50q2 = 0

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

Divide each side by '50'.
-1.56 + 2.5q + q2 = 0.0

Move the constant term to the right:

Add '1.56' to each side of the equation.
-1.56 + 2.5q + 1.56 + q2 = 0.0 + 1.56

Reorder the terms:
-1.56 + 1.56 + 2.5q + q2 = 0.0 + 1.56

Combine like terms: -1.56 + 1.56 = 0.00
0.00 + 2.5q + q2 = 0.0 + 1.56
2.5q + q2 = 0.0 + 1.56

Combine like terms: 0.0 + 1.56 = 1.56
2.5q + q2 = 1.56

The q term is 2.5q.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5q + 1.5625 + q2 = 1.56 + 1.5625

Reorder the terms:
1.5625 + 2.5q + q2 = 1.56 + 1.5625

Combine like terms: 1.56 + 1.5625 = 3.1225
1.5625 + 2.5q + q2 = 3.1225

Factor a perfect square on the left side:
(q + 1.25)(q + 1.25) = 3.1225

Calculate the square root of the right side: 1.767059705

Break this problem into two subproblems by setting 
(q + 1.25) equal to 1.767059705 and -1.767059705.

Subproblem 1
q + 1.25 = 1.767059705

Simplifying
q + 1.25 = 1.767059705

Reorder the terms:
1.25 + q = 1.767059705

Solving
1.25 + q = 1.767059705

Solving for variable 'q'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + q = 1.767059705 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + q = 1.767059705 + -1.25
q = 1.767059705 + -1.25

Combine like terms: 1.767059705 + -1.25 = 0.517059705
q = 0.517059705

Simplifying
q = 0.517059705

Subproblem 2
q + 1.25 = -1.767059705

Simplifying
q + 1.25 = -1.767059705

Reorder the terms:
1.25 + q = -1.767059705

Solving
1.25 + q = -1.767059705

Solving for variable 'q'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + q = -1.767059705 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + q = -1.767059705 + -1.25
q = -1.767059705 + -1.25

Combine like terms: -1.767059705 + -1.25 = -3.017059705
q = -3.017059705

Simplifying
q = -3.017059705

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.517059705, -3.017059705}
Solution
q = {0.517059705, -3.017059705}