The equation you've provided is a quadratic equation in the form:

$Ax^2 + bx + (b - c) = 0$

Here, $A$, $b$, and $c$ are constants, and the variable $x$ represents the unknown. To solve for $x$, you can use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4AC}}{2A}$

In your case, $A$ is already given, $b$ is the coefficient of $x$, and $C = b - c$.

So, the solution for $x$ becomes:

$x = \frac{-b \pm \sqrt{b^2 - 4A(b - c)}}{2A}$

This will give you two possible values for $x$, depending on the discriminant $b^2 - 4A(b - c)$.

Would you like to go deeper into this solution, or need any specific values to substitute in? Let me know if you have any further questions!

Here are some related questions you might want to explore:

1. What is the discriminant in a quadratic equation, and what does it tell us about the roots?
2. How do you solve quadratic equations when the discriminant is negative?
3. What are the different methods to solve quadratic equations besides the quadratic formula?
4. How do you determine the nature of the roots of a quadratic equation?
5. Can a quadratic equation have only one solution? How is that possible?

Tip: If you're solving a quadratic equation and the discriminant is negative, the solutions will be complex numbers (involving $i$, the imaginary unit).