The expression you provided is the quadratic formula, which is used to find the solutions of a quadratic equation of the form \( ax^2 + bx + c = 0 \). Here's the formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

### Explanation:
- **\( a \)**: The coefficient of \( x^2 \).
- **\( b \)**: The coefficient of \( x \).
- **\( c \)**: The constant term.
- **\( \pm \)**: Indicates that there are generally two solutions, one with the plus sign and one with the minus sign.
- **\( \sqrt{b^2 - 4ac} \)**: The discriminant, which determines the nature of the roots:
  - If \( b^2 - 4ac > 0 \), there are two distinct real roots.
  - If \( b^2 - 4ac = 0 \), there is one real root (a repeated root).
  - If \( b^2 - 4ac < 0 \), there are two complex roots.

Would you like more details or have any specific questions?

### Related Questions:
1. How can you derive the quadratic formula from completing the square?
2. What are some examples of quadratic equations where the discriminant is negative?
3. How does the discriminant determine the nature of the roots?
4. Can the quadratic formula be used for higher-degree polynomials?
5. How do you factor a quadratic equation instead of using the quadratic formula?

**Tip:** Always check the discriminant first before solving with the quadratic formula, as it gives insight into the nature of the roots.

Explore the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a) and its application in solving quadratic equations. Learn about the discriminant theorem and how it determines the nature of roots. Suitable for students in Grades 9-12.

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