0.85*x*2000*20*(826-0.425*x)=2400000

Solution for 0.85*x*2000*20*(826-0.425*x)=2400000 equation:

Simplifying
0.85x * 2000 * 20(826 + -0.425x) = 2400000

Reorder the terms for easier multiplication:
0.85 * 2000 * 20x(826 + -0.425x) = 2400000

Multiply 0.85 * 2000
1700 * 20x(826 + -0.425x) = 2400000

Multiply 1700 * 20
34000x(826 + -0.425x) = 2400000
(826 * 34000x + -0.425x * 34000x) = 2400000
(28084000x + -14450x2) = 2400000

Solving
28084000x + -14450x2 = 2400000

Solving for variable 'x'.

Reorder the terms:
-2400000 + 28084000x + -14450x2 = 2400000 + -2400000

Combine like terms: 2400000 + -2400000 = 0
-2400000 + 28084000x + -14450x2 = 0

Factor out the Greatest Common Factor (GCF), '50'.
50(-48000 + 561680x + -289x2) = 0

Ignore the factor 50.
Subproblem 1
Set the factor '(-48000 + 561680x + -289x2)' equal to zero and attempt to solve:

Simplifying
-48000 + 561680x + -289x2 = 0

Solving
-48000 + 561680x + -289x2 = 0

Begin completing the square.  Divide all terms by
-289 the coefficient of the squared term: 

Divide each side by '-289'.
166.0899654 + -1943.529412x + x2 = 0

Move the constant term to the right:

Add '-166.0899654' to each side of the equation.
166.0899654 + -1943.529412x + -166.0899654 + x2 = 0 + -166.0899654

Reorder the terms:
166.0899654 + -166.0899654 + -1943.529412x + x2 = 0 + -166.0899654

Combine like terms: 166.0899654 + -166.0899654 = 0.0000000
0.0000000 + -1943.529412x + x2 = 0 + -166.0899654
-1943.529412x + x2 = 0 + -166.0899654

Combine like terms: 0 + -166.0899654 = -166.0899654
-1943.529412x + x2 = -166.0899654

The x term is -1943.529412x.  Take half its coefficient (-971.764706).
Square it (944326.6438) and add it to both sides.

Add '944326.6438' to each side of the equation.
-1943.529412x + 944326.6438 + x2 = -166.0899654 + 944326.6438

Reorder the terms:
944326.6438 + -1943.529412x + x2 = -166.0899654 + 944326.6438

Combine like terms: -166.0899654 + 944326.6438 = 944160.5538346
944326.6438 + -1943.529412x + x2 = 944160.5538346

Factor a perfect square on the left side:
(x + -971.764706)(x + -971.764706) = 944160.5538346

Calculate the square root of the right side: 971.679244316

Break this problem into two subproblems by setting 
(x + -971.764706) equal to 971.679244316 and -971.679244316.

Subproblem 1
x + -971.764706 = 971.679244316

Simplifying
x + -971.764706 = 971.679244316

Reorder the terms:
-971.764706 + x = 971.679244316

Solving
-971.764706 + x = 971.679244316

Solving for variable 'x'.

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

Add '971.764706' to each side of the equation.
-971.764706 + 971.764706 + x = 971.679244316 + 971.764706

Combine like terms: -971.764706 + 971.764706 = 0.000000
0.000000 + x = 971.679244316 + 971.764706
x = 971.679244316 + 971.764706

Combine like terms: 971.679244316 + 971.764706 = 1943.443950316
x = 1943.443950316

Simplifying
x = 1943.443950316

Subproblem 2
x + -971.764706 = -971.679244316

Simplifying
x + -971.764706 = -971.679244316

Reorder the terms:
-971.764706 + x = -971.679244316

Solving
-971.764706 + x = -971.679244316

Solving for variable 'x'.

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

Add '971.764706' to each side of the equation.
-971.764706 + 971.764706 + x = -971.679244316 + 971.764706

Combine like terms: -971.764706 + 971.764706 = 0.000000
0.000000 + x = -971.679244316 + 971.764706
x = -971.679244316 + 971.764706

Combine like terms: -971.679244316 + 971.764706 = 0.085461684
x = 0.085461684

Simplifying
x = 0.085461684

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1943.443950316, 0.085461684}
Solution
x = {1943.443950316, 0.085461684}