-x^2+2400x-1320000=0

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Solution for -x^2+2400x-1320000=0 equation: 


Simplifying
-1x2 + 2400x + -1320000 = 0

Reorder the terms:
-1320000 + 2400x + -1x2 = 0

Solving
-1320000 + 2400x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1320000 + -2400x + x2 = 0

Move the constant term to the right:

Add '-1320000' to each side of the equation.
1320000 + -2400x + -1320000 + x2 = 0 + -1320000

Reorder the terms:
1320000 + -1320000 + -2400x + x2 = 0 + -1320000

Combine like terms: 1320000 + -1320000 = 0
0 + -2400x + x2 = 0 + -1320000
-2400x + x2 = 0 + -1320000

Combine like terms: 0 + -1320000 = -1320000
-2400x + x2 = -1320000

The x term is -2400x.  Take half its coefficient (-1200).
Square it (1440000) and add it to both sides.

Add '1440000' to each side of the equation.
-2400x + 1440000 + x2 = -1320000 + 1440000

Reorder the terms:
1440000 + -2400x + x2 = -1320000 + 1440000

Combine like terms: -1320000 + 1440000 = 120000
1440000 + -2400x + x2 = 120000

Factor a perfect square on the left side:
(x + -1200)(x + -1200) = 120000

Calculate the square root of the right side: 346.410161514

Break this problem into two subproblems by setting 
(x + -1200) equal to 346.410161514 and -346.410161514.


Subproblem 1
x + -1200 = 346.410161514

Simplifying
x + -1200 = 346.410161514

Reorder the terms:
-1200 + x = 346.410161514

Solving
-1200 + x = 346.410161514

Solving for variable 'x'.

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

Add '1200' to each side of the equation.
-1200 + 1200 + x = 346.410161514 + 1200

Combine like terms: -1200 + 1200 = 0
0 + x = 346.410161514 + 1200
x = 346.410161514 + 1200

Combine like terms: 346.410161514 + 1200 = 1546.410161514
x = 1546.410161514

Simplifying
x = 1546.410161514


Subproblem 2
x + -1200 = -346.410161514

Simplifying
x + -1200 = -346.410161514

Reorder the terms:
-1200 + x = -346.410161514

Solving
-1200 + x = -346.410161514

Solving for variable 'x'.

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

Add '1200' to each side of the equation.
-1200 + 1200 + x = -346.410161514 + 1200

Combine like terms: -1200 + 1200 = 0
0 + x = -346.410161514 + 1200
x = -346.410161514 + 1200

Combine like terms: -346.410161514 + 1200 = 853.589838486
x = 853.589838486

Simplifying
x = 853.589838486


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1546.410161514, 853.589838486}

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