To solve the quadratic equation \(4x^2 - 15x + 7\), we can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
where \(a = 4\), \(b = -15\), and \(c = 7\).

1. Calculate the discriminant (\(b^2 - 4ac\)):
\[ (-15)^2 - 4 \cdot 4 \cdot 7 = 225 - 112 = 113 \]

2. Substitute the values into the quadratic formula:
\[ x = \frac{15 \pm \sqrt{113}}{8} \]

Therefore, the solutions are:
\[ x = \frac{15 + \sqrt{113}}{8} \]
\[ x = \frac{15 - \sqrt{113}}{8} \]

Would you like more details or have any questions?

Here are some questions you might find useful:
1. How do I simplify the square root in the quadratic formula?
2. Can you show a step-by-step solution for another quadratic equation?
3. What are the real-life applications of solving quadratic equations?
4. How do you factor a quadratic equation?
5. Can you explain how to complete the square for this equation?

**Tip:** When using the quadratic formula, always check the discriminant (\(b^2 - 4ac\)) first. If it is negative, the equation has complex roots.

Learn how to solve the quadratic equation 4x^2 - 15x + 7 with a detailed step-by-step solution using the quadratic formula. Explore the discriminant and the process of finding both real roots. Suitable for high school students studying algebra.

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