## Solving the Equation: (5x-9)(x-1)-x(x-2)=0

This article will guide you through the process of solving the given quadratic equation: **(5x-9)(x-1)-x(x-2)=0**.

### Step 1: Expand the Equation

First, we need to expand the equation by multiplying out the brackets:

**(5x-9)(x-1) = 5x² - 5x - 9x + 9 = 5x² - 14x + 9****x(x-2) = x² - 2x**

Now our equation looks like this: **5x² - 14x + 9 - (x² - 2x) = 0**

### Step 2: Simplify the Equation

Next, we simplify the equation by combining like terms:

**5x² - x² - 14x + 2x + 9 = 0****4x² - 12x + 9 = 0**

### Step 3: Solve for x

We can now solve for x using the quadratic formula. The quadratic formula is:

**x = (-b ± √(b² - 4ac)) / 2a**

Where:

- a = 4
- b = -12
- c = 9

Substituting these values into the quadratic formula, we get:

**x = (12 ± √((-12)² - 4 * 4 * 9)) / (2 * 4)**

**x = (12 ± √(144 - 144)) / 8**

**x = (12 ± √0) / 8**

**x = 12 / 8**

**x = 3/2**

Therefore, the solution to the equation **(5x-9)(x-1)-x(x-2)=0** is **x = 3/2**.

### Conclusion

By following the steps outlined above, we successfully solved the quadratic equation. Remember, the quadratic formula is a powerful tool for solving equations of this type. Always ensure you simplify and expand the equation correctly to avoid errors.