To solve for x, we can start by simplifying the equation:
7500 / (2x + 10) = 7500 / x + 500
Cross multiply to get rid of the fractions:
7500x = 7500(2x + 10) + 500x(2x + 10)
7500x = 15000x + 75000 + 1000x^2 + 5000x
Rearrange the terms to set the equation equal to zero:
1000x^2 - 7500x + 75000 + 5000x = 0
1000x^2 - 2500x + 75000 = 0
Divide the entire equation by 500 to simplify:
2x^2 - 5x + 150 = 0
Now, we can use the quadratic formula to solve for x:
x = (-(-5) ± sqrt((-5)^2 - 4(2)(150))) / 2(2)
x = (5 ± sqrt(25 - 1200)) / 4
x = (5 ± sqrt(-1175)) / 4
Since the square root of a negative number is not a real number, the equation has no real solutions.
To solve for x, we can start by simplifying the equation:
7500 / (2x + 10) = 7500 / x + 500
Cross multiply to get rid of the fractions:
7500x = 7500(2x + 10) + 500x(2x + 10)
7500x = 15000x + 75000 + 1000x^2 + 5000x
Rearrange the terms to set the equation equal to zero:
1000x^2 - 7500x + 75000 + 5000x = 0
1000x^2 - 2500x + 75000 = 0
Divide the entire equation by 500 to simplify:
2x^2 - 5x + 150 = 0
Now, we can use the quadratic formula to solve for x:
x = (-(-5) ± sqrt((-5)^2 - 4(2)(150))) / 2(2)
x = (5 ± sqrt(25 - 1200)) / 4
x = (5 ± sqrt(-1175)) / 4
Since the square root of a negative number is not a real number, the equation has no real solutions.