-0.003x^2+128x+9000=0

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Solution for -0.003x^2+128x+9000=0 equation: 


Simplifying
-0.003x2 + 128x + 9000 = 0

Reorder the terms:
9000 + 128x + -0.003x2 = 0

Solving
9000 + 128x + -0.003x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.003 the coefficient of the squared term: 

Divide each side by '-0.003'.
-3000000 + -42666.66667x + x2 = 0

Move the constant term to the right:

Add '3000000' to each side of the equation.
-3000000 + -42666.66667x + 3000000 + x2 = 0 + 3000000

Reorder the terms:
-3000000 + 3000000 + -42666.66667x + x2 = 0 + 3000000

Combine like terms: -3000000 + 3000000 = 0
0 + -42666.66667x + x2 = 0 + 3000000
-42666.66667x + x2 = 0 + 3000000

Combine like terms: 0 + 3000000 = 3000000
-42666.66667x + x2 = 3000000

The x term is -42666.66667x.  Take half its coefficient (-21333.33334).
Square it (455111111.4) and add it to both sides.

Add '455111111.4' to each side of the equation.
-42666.66667x + 455111111.4 + x2 = 3000000 + 455111111.4

Reorder the terms:
455111111.4 + -42666.66667x + x2 = 3000000 + 455111111.4

Combine like terms: 3000000 + 455111111.4 = 458111111.4
455111111.4 + -42666.66667x + x2 = 458111111.4

Factor a perfect square on the left side:
(x + -21333.33334)(x + -21333.33334) = 458111111.4

Calculate the square root of the right side: 21403.530348987

Break this problem into two subproblems by setting 
(x + -21333.33334) equal to 21403.530348987 and -21403.530348987.


Subproblem 1
x + -21333.33334 = 21403.530348987

Simplifying
x + -21333.33334 = 21403.530348987

Reorder the terms:
-21333.33334 + x = 21403.530348987

Solving
-21333.33334 + x = 21403.530348987

Solving for variable 'x'.

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

Add '21333.33334' to each side of the equation.
-21333.33334 + 21333.33334 + x = 21403.530348987 + 21333.33334

Combine like terms: -21333.33334 + 21333.33334 = 0.00000
0.00000 + x = 21403.530348987 + 21333.33334
x = 21403.530348987 + 21333.33334

Combine like terms: 21403.530348987 + 21333.33334 = 42736.863688987
x = 42736.863688987

Simplifying
x = 42736.863688987


Subproblem 2
x + -21333.33334 = -21403.530348987

Simplifying
x + -21333.33334 = -21403.530348987

Reorder the terms:
-21333.33334 + x = -21403.530348987

Solving
-21333.33334 + x = -21403.530348987

Solving for variable 'x'.

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

Add '21333.33334' to each side of the equation.
-21333.33334 + 21333.33334 + x = -21403.530348987 + 21333.33334

Combine like terms: -21333.33334 + 21333.33334 = 0.00000
0.00000 + x = -21403.530348987 + 21333.33334
x = -21403.530348987 + 21333.33334

Combine like terms: -21403.530348987 + 21333.33334 = -70.197008987
x = -70.197008987

Simplifying
x = -70.197008987


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42736.863688987, -70.197008987}

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