150000=-20x^2+5000x

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Solution for 150000=-20x^2+5000x equation: 


Simplifying
150000 = -20x2 + 5000x

Reorder the terms:
150000 = 5000x + -20x2

Solving
150000 = 5000x + -20x2

Solving for variable 'x'.

Reorder the terms:
150000 + -5000x + 20x2 = 5000x + -5000x + -20x2 + 20x2

Combine like terms: 5000x + -5000x = 0
150000 + -5000x + 20x2 = 0 + -20x2 + 20x2
150000 + -5000x + 20x2 = -20x2 + 20x2

Combine like terms: -20x2 + 20x2 = 0
150000 + -5000x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(7500 + -250x + x2) = 0

Ignore the factor 20.

Subproblem 1
Set the factor '(7500 + -250x + x2)' equal to zero and attempt to solve:

Simplifying
7500 + -250x + x2 = 0

Solving
7500 + -250x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7500' to each side of the equation.
7500 + -250x + -7500 + x2 = 0 + -7500

Reorder the terms:
7500 + -7500 + -250x + x2 = 0 + -7500

Combine like terms: 7500 + -7500 = 0
0 + -250x + x2 = 0 + -7500
-250x + x2 = 0 + -7500

Combine like terms: 0 + -7500 = -7500
-250x + x2 = -7500

The x term is -250x.  Take half its coefficient (-125).
Square it (15625) and add it to both sides.

Add '15625' to each side of the equation.
-250x + 15625 + x2 = -7500 + 15625

Reorder the terms:
15625 + -250x + x2 = -7500 + 15625

Combine like terms: -7500 + 15625 = 8125
15625 + -250x + x2 = 8125

Factor a perfect square on the left side:
(x + -125)(x + -125) = 8125

Calculate the square root of the right side: 90.138781887

Break this problem into two subproblems by setting 
(x + -125) equal to 90.138781887 and -90.138781887.


Subproblem 1
x + -125 = 90.138781887

Simplifying
x + -125 = 90.138781887

Reorder the terms:
-125 + x = 90.138781887

Solving
-125 + x = 90.138781887

Solving for variable 'x'.

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

Add '125' to each side of the equation.
-125 + 125 + x = 90.138781887 + 125

Combine like terms: -125 + 125 = 0
0 + x = 90.138781887 + 125
x = 90.138781887 + 125

Combine like terms: 90.138781887 + 125 = 215.138781887
x = 215.138781887

Simplifying
x = 215.138781887


Subproblem 2
x + -125 = -90.138781887

Simplifying
x + -125 = -90.138781887

Reorder the terms:
-125 + x = -90.138781887

Solving
-125 + x = -90.138781887

Solving for variable 'x'.

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

Add '125' to each side of the equation.
-125 + 125 + x = -90.138781887 + 125

Combine like terms: -125 + 125 = 0
0 + x = -90.138781887 + 125
x = -90.138781887 + 125

Combine like terms: -90.138781887 + 125 = 34.861218113
x = 34.861218113

Simplifying
x = 34.861218113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {215.138781887, 34.861218113}
Solution
x = {215.138781887, 34.861218113}

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