## Solving for the Value of b-a

We are given the equation:
**(8x^2-15x)-(x^2-27x) = ax^2 + bx**

To find the value of **b-a**, we need to simplify the equation and identify the coefficients of the x^2 and x terms.

**1. Simplify the Equation:**

First, distribute the negative sign in the second part of the equation: 8x^2 - 15x - x^2 + 27x = ax^2 + bx

Now combine like terms: 7x^2 + 12x = ax^2 + bx

**2. Identify the Coefficients:**

By comparing both sides of the equation, we can see:

**a = 7**(coefficient of x^2 on the left side)**b = 12**(coefficient of x on the left side)

**3. Calculate b-a:**

Finally, substitute the values we found:
b - a = 12 - 7 = **5**

Therefore, the value of b-a is **5**.