6x^2-300x=50000+300x-3x^2

Solution for 6x^2-300x=50000+300x-3x^2 equation:

Simplifying
6x2 + -300x = 50000 + 300x + -3x2

Reorder the terms:
-300x + 6x2 = 50000 + 300x + -3x2

Solving
-300x + 6x2 = 50000 + 300x + -3x2

Solving for variable 'x'.

Reorder the terms:
-50000 + -300x + -300x + 6x2 + 3x2 = 50000 + 300x + -3x2 + -50000 + -300x + 3x2

Combine like terms: -300x + -300x = -600x
-50000 + -600x + 6x2 + 3x2 = 50000 + 300x + -3x2 + -50000 + -300x + 3x2

Combine like terms: 6x2 + 3x2 = 9x2
-50000 + -600x + 9x2 = 50000 + 300x + -3x2 + -50000 + -300x + 3x2

Reorder the terms:
-50000 + -600x + 9x2 = 50000 + -50000 + 300x + -300x + -3x2 + 3x2

Combine like terms: 50000 + -50000 = 0
-50000 + -600x + 9x2 = 0 + 300x + -300x + -3x2 + 3x2
-50000 + -600x + 9x2 = 300x + -300x + -3x2 + 3x2

Combine like terms: 300x + -300x = 0
-50000 + -600x + 9x2 = 0 + -3x2 + 3x2
-50000 + -600x + 9x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-50000 + -600x + 9x2 = 0

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

Divide each side by '9'.
-5555.555556 + -66.66666667x + x2 = 0

Move the constant term to the right:

Add '5555.555556' to each side of the equation.
-5555.555556 + -66.66666667x + 5555.555556 + x2 = 0 + 5555.555556

Reorder the terms:
-5555.555556 + 5555.555556 + -66.66666667x + x2 = 0 + 5555.555556

Combine like terms: -5555.555556 + 5555.555556 = 0.000000
0.000000 + -66.66666667x + x2 = 0 + 5555.555556
-66.66666667x + x2 = 0 + 5555.555556

Combine like terms: 0 + 5555.555556 = 5555.555556
-66.66666667x + x2 = 5555.555556

The x term is -66.66666667x.  Take half its coefficient (-33.33333334).
Square it (1111.111112) and add it to both sides.

Add '1111.111112' to each side of the equation.
-66.66666667x + 1111.111112 + x2 = 5555.555556 + 1111.111112

Reorder the terms:
1111.111112 + -66.66666667x + x2 = 5555.555556 + 1111.111112

Combine like terms: 5555.555556 + 1111.111112 = 6666.666668
1111.111112 + -66.66666667x + x2 = 6666.666668

Factor a perfect square on the left side:
(x + -33.33333334)(x + -33.33333334) = 6666.666668

Calculate the square root of the right side: 81.649658101

Break this problem into two subproblems by setting 
(x + -33.33333334) equal to 81.649658101 and -81.649658101.

Subproblem 1
x + -33.33333334 = 81.649658101

Simplifying
x + -33.33333334 = 81.649658101

Reorder the terms:
-33.33333334 + x = 81.649658101

Solving
-33.33333334 + x = 81.649658101

Solving for variable 'x'.

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

Add '33.33333334' to each side of the equation.
-33.33333334 + 33.33333334 + x = 81.649658101 + 33.33333334

Combine like terms: -33.33333334 + 33.33333334 = 0.00000000
0.00000000 + x = 81.649658101 + 33.33333334
x = 81.649658101 + 33.33333334

Combine like terms: 81.649658101 + 33.33333334 = 114.982991441
x = 114.982991441

Simplifying
x = 114.982991441

Subproblem 2
x + -33.33333334 = -81.649658101

Simplifying
x + -33.33333334 = -81.649658101

Reorder the terms:
-33.33333334 + x = -81.649658101

Solving
-33.33333334 + x = -81.649658101

Solving for variable 'x'.

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

Add '33.33333334' to each side of the equation.
-33.33333334 + 33.33333334 + x = -81.649658101 + 33.33333334

Combine like terms: -33.33333334 + 33.33333334 = 0.00000000
0.00000000 + x = -81.649658101 + 33.33333334
x = -81.649658101 + 33.33333334

Combine like terms: -81.649658101 + 33.33333334 = -48.316324761
x = -48.316324761

Simplifying
x = -48.316324761

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {114.982991441, -48.316324761}