## Solving a Quadratic Equation: (8x²−15x)−(x2−27x)=ax²+bx

This article will guide you through solving the quadratic equation (8x²−15x)−(x2−27x)=ax²+bx and finding the values of *a* and *b*.

### Step 1: Simplify the Equation

First, we need to simplify the equation by removing the parentheses and combining like terms:

(8x²−15x)−(x²−27x) = 8x² - 15x - x² + 27x = 7x² + 12x

Therefore, the simplified equation becomes: **7x² + 12x = ax² + bx**

### Step 2: Matching Coefficients

Now, we need to match the coefficients of the corresponding terms on both sides of the equation:

**Coefficients of x²:**7 = a**Coefficients of x:**12 = b

### Step 3: Solution

We have now determined the values of *a* and *b*:

**a = 7****b = 12**

Therefore, the solution to the equation is: **(8x²−15x)−(x2−27x)=7x² + 12x**

### Conclusion

By simplifying the equation and matching the coefficients, we were able to solve for the values of *a* and *b*. This process demonstrates how to manipulate algebraic expressions to achieve a desired outcome.