10=-50x^2+6000x

Solution for 10=-50x^2+6000x equation:

Simplifying
10 = -50x2 + 6000x

Reorder the terms:
10 = 6000x + -50x2

Solving
10 = 6000x + -50x2

Solving for variable 'x'.

Reorder the terms:
10 + -6000x + 50x2 = 6000x + -6000x + -50x2 + 50x2

Combine like terms: 6000x + -6000x = 0
10 + -6000x + 50x2 = 0 + -50x2 + 50x2
10 + -6000x + 50x2 = -50x2 + 50x2

Combine like terms: -50x2 + 50x2 = 0
10 + -6000x + 50x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(1 + -600x + 5x2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(1 + -600x + 5x2)' equal to zero and attempt to solve:

Simplifying
1 + -600x + 5x2 = 0

Solving
1 + -600x + 5x2 = 0

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

Divide each side by '5'.
0.2 + -120x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -120x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -120x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -120x + x2 = 0 + -0.2
-120x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-120x + x2 = -0.2

The x term is -120x.  Take half its coefficient (-60).
Square it (3600) and add it to both sides.

Add '3600' to each side of the equation.
-120x + 3600 + x2 = -0.2 + 3600

Reorder the terms:
3600 + -120x + x2 = -0.2 + 3600

Combine like terms: -0.2 + 3600 = 3599.8
3600 + -120x + x2 = 3599.8

Factor a perfect square on the left side:
(x + -60)(x + -60) = 3599.8

Calculate the square root of the right side: 59.99833331

Break this problem into two subproblems by setting 
(x + -60) equal to 59.99833331 and -59.99833331.

Subproblem 1
x + -60 = 59.99833331

Simplifying
x + -60 = 59.99833331

Reorder the terms:
-60 + x = 59.99833331

Solving
-60 + x = 59.99833331

Solving for variable 'x'.

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

Add '60' to each side of the equation.
-60 + 60 + x = 59.99833331 + 60

Combine like terms: -60 + 60 = 0
0 + x = 59.99833331 + 60
x = 59.99833331 + 60

Combine like terms: 59.99833331 + 60 = 119.99833331
x = 119.99833331

Simplifying
x = 119.99833331

Subproblem 2
x + -60 = -59.99833331

Simplifying
x + -60 = -59.99833331

Reorder the terms:
-60 + x = -59.99833331

Solving
-60 + x = -59.99833331

Solving for variable 'x'.

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

Add '60' to each side of the equation.
-60 + 60 + x = -59.99833331 + 60

Combine like terms: -60 + 60 = 0
0 + x = -59.99833331 + 60
x = -59.99833331 + 60

Combine like terms: -59.99833331 + 60 = 0.00166669
x = 0.00166669

Simplifying
x = 0.00166669

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {119.99833331, 0.00166669}
Solution
x = {119.99833331, 0.00166669}