To solve the quadratic equation \(4x^2 - 15x - 503\), we will use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
where \(a = 4\), \(b = -15\), and \(c = -503\).

1. Calculate the discriminant (\(b^2 - 4ac\)):
\[ (-15)^2 - 4 \cdot 4 \cdot (-503) = 225 + 8048 = 8273 \]

2. Substitute the values into the quadratic formula:
\[ x = \frac{15 \pm \sqrt{8273}}{8} \]

Therefore, the solutions are:
\[ x = \frac{15 + \sqrt{8273}}{8} \]
\[ x = \frac{15 - \sqrt{8273}}{8} \]

Would you like more details or have any questions?

Here are some questions you might find useful:
1. How do you approximate the value of \(\sqrt{8273}\)?
2. Can you solve a quadratic equation by factoring instead of using the quadratic formula?
3. What are the steps to complete the square for this equation?
4. How can you determine if a quadratic equation has real or complex roots?
5. What are some methods to graph a quadratic equation?

**Tip:** Always simplify the discriminant first to determine the nature of the roots (real or complex) before proceeding with the quadratic formula.

Learn how to solve the quadratic equation 4x^2 - 15x - 503 with a detailed step-by-step solution using the quadratic formula. Understand the concept of discriminant and its role in determining the nature of roots. Suitable for high school students (Grades 10-12).

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