7.5x^2-64989x+500000=0

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Solution for 7.5x^2-64989x+500000=0 equation: 


Simplifying
7.5x2 + -64989x + 500000 = 0

Reorder the terms:
500000 + -64989x + 7.5x2 = 0

Solving
500000 + -64989x + 7.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '7.5'.
66666.66667 + -8665.2x + x2 = 0

Move the constant term to the right:

Add '-66666.66667' to each side of the equation.
66666.66667 + -8665.2x + -66666.66667 + x2 = 0 + -66666.66667

Reorder the terms:
66666.66667 + -66666.66667 + -8665.2x + x2 = 0 + -66666.66667

Combine like terms: 66666.66667 + -66666.66667 = 0.00000
0.00000 + -8665.2x + x2 = 0 + -66666.66667
-8665.2x + x2 = 0 + -66666.66667

Combine like terms: 0 + -66666.66667 = -66666.66667
-8665.2x + x2 = -66666.66667

The x term is -8665.2x.  Take half its coefficient (-4332.6).
Square it (18771422.76) and add it to both sides.

Add '18771422.76' to each side of the equation.
-8665.2x + 18771422.76 + x2 = -66666.66667 + 18771422.76

Reorder the terms:
18771422.76 + -8665.2x + x2 = -66666.66667 + 18771422.76

Combine like terms: -66666.66667 + 18771422.76 = 18704756.09333
18771422.76 + -8665.2x + x2 = 18704756.09333

Factor a perfect square on the left side:
(x + -4332.6)(x + -4332.6) = 18704756.09333

Calculate the square root of the right side: 4324.899547195

Break this problem into two subproblems by setting 
(x + -4332.6) equal to 4324.899547195 and -4324.899547195.


Subproblem 1
x + -4332.6 = 4324.899547195

Simplifying
x + -4332.6 = 4324.899547195

Reorder the terms:
-4332.6 + x = 4324.899547195

Solving
-4332.6 + x = 4324.899547195

Solving for variable 'x'.

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

Add '4332.6' to each side of the equation.
-4332.6 + 4332.6 + x = 4324.899547195 + 4332.6

Combine like terms: -4332.6 + 4332.6 = 0.0
0.0 + x = 4324.899547195 + 4332.6
x = 4324.899547195 + 4332.6

Combine like terms: 4324.899547195 + 4332.6 = 8657.499547195
x = 8657.499547195

Simplifying
x = 8657.499547195


Subproblem 2
x + -4332.6 = -4324.899547195

Simplifying
x + -4332.6 = -4324.899547195

Reorder the terms:
-4332.6 + x = -4324.899547195

Solving
-4332.6 + x = -4324.899547195

Solving for variable 'x'.

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

Add '4332.6' to each side of the equation.
-4332.6 + 4332.6 + x = -4324.899547195 + 4332.6

Combine like terms: -4332.6 + 4332.6 = 0.0
0.0 + x = -4324.899547195 + 4332.6
x = -4324.899547195 + 4332.6

Combine like terms: -4324.899547195 + 4332.6 = 7.700452805
x = 7.700452805

Simplifying
x = 7.700452805


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8657.499547195, 7.700452805}

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