20x^2-2100x-13000=0

Solution for 20x^2-2100x-13000=0 equation:

Simplifying
20x2 + -2100x + -13000 = 0

Reorder the terms:
-13000 + -2100x + 20x2 = 0

Solving
-13000 + -2100x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-650 + -105x + x2) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(-650 + -105x + x2)' equal to zero and attempt to solve:

Simplifying
-650 + -105x + x2 = 0

Solving
-650 + -105x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '650' to each side of the equation.
-650 + -105x + 650 + x2 = 0 + 650

Reorder the terms:
-650 + 650 + -105x + x2 = 0 + 650

Combine like terms: -650 + 650 = 0
0 + -105x + x2 = 0 + 650
-105x + x2 = 0 + 650

Combine like terms: 0 + 650 = 650
-105x + x2 = 650

The x term is -105x.  Take half its coefficient (-52.5).
Square it (2756.25) and add it to both sides.

Add '2756.25' to each side of the equation.
-105x + 2756.25 + x2 = 650 + 2756.25

Reorder the terms:
2756.25 + -105x + x2 = 650 + 2756.25

Combine like terms: 650 + 2756.25 = 3406.25
2756.25 + -105x + x2 = 3406.25

Factor a perfect square on the left side:
(x + -52.5)(x + -52.5) = 3406.25

Calculate the square root of the right side: 58.36308765

Break this problem into two subproblems by setting 
(x + -52.5) equal to 58.36308765 and -58.36308765.

Subproblem 1
x + -52.5 = 58.36308765

Simplifying
x + -52.5 = 58.36308765

Reorder the terms:
-52.5 + x = 58.36308765

Solving
-52.5 + x = 58.36308765

Solving for variable 'x'.

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

Add '52.5' to each side of the equation.
-52.5 + 52.5 + x = 58.36308765 + 52.5

Combine like terms: -52.5 + 52.5 = 0.0
0.0 + x = 58.36308765 + 52.5
x = 58.36308765 + 52.5

Combine like terms: 58.36308765 + 52.5 = 110.86308765
x = 110.86308765

Simplifying
x = 110.86308765

Subproblem 2
x + -52.5 = -58.36308765

Simplifying
x + -52.5 = -58.36308765

Reorder the terms:
-52.5 + x = -58.36308765

Solving
-52.5 + x = -58.36308765

Solving for variable 'x'.

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

Add '52.5' to each side of the equation.
-52.5 + 52.5 + x = -58.36308765 + 52.5

Combine like terms: -52.5 + 52.5 = 0.0
0.0 + x = -58.36308765 + 52.5
x = -58.36308765 + 52.5

Combine like terms: -58.36308765 + 52.5 = -5.86308765
x = -5.86308765

Simplifying
x = -5.86308765

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {110.86308765, -5.86308765}
Solution
x = {110.86308765, -5.86308765}