Question

2) 9x - 15 = 2/x - 24​

Answer 1

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Answer 2

To solve the equation 9x - 15 = 2/x - 24, you can follow these steps:

1. First, eliminate the fraction by multiplying both sides of the equation by x to get rid of the denominator: 9x^2 - 15x = 2 - 24x

2. Move all terms to one side of the equation to set it equal to zero: 9x^2 - 15x + 24x - 2 = 0

3. Combine like terms: 9x^2 + 9x - 2 = 0

4. Now, you have a quadratic equation in the form ax^2 + bx + c = 0, where a = 9, b = 9, and c = -2.

5. You can solve this quadratic equation using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

   Plugging in the values for a, b, and c: x = (-9 ± √(9^2 - 4 * 9 * (-2))) / (2 * 9)

6. Calculate the discriminant (the value inside the square root): Discriminant = 9^2 - 4 * 9 * (-2) = 81 + 72 = 153

7. Now, plug the discriminant back into the quadratic formula: x = (-9 ± √153) / (2 * 9)

8. You can simplify this expression further: x = (-9 ± √(9 * 17)) / 18

9. Divide both the numerator and denominator by 9: x = (-1 ± √(17)) / 2

So, the solutions to the equation 9x - 15 = 2/x - 24 are: x = (-1 + √17)/2 x = (-1 - √17)/2