To solve the quadratic equation \(4x^2 - 16x + 15 = 0\), we can use the **quadratic formula**:

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

For the given equation \(4x^2 - 16x + 15 = 0\), the coefficients are:
- \(a = 4\)
- \(b = -16\)
- \(c = 15\)

### Step 1: Calculate the discriminant
\[
\Delta = b^2 - 4ac = (-16)^2 - 4(4)(15) = 256 - 240 = 16
\]

### Step 2: Apply the quadratic formula
\[
x = \frac{-(-16) \pm \sqrt{16}}{2(4)} = \frac{16 \pm 4}{8}
\]

### Step 3: Solve for the two possible values of \(x\)
\[
x_1 = \frac{16 + 4}{8} = \frac{20}{8} = 2.5
\]
\[
x_2 = \frac{16 - 4}{8} = \frac{12}{8} = 1.5
\]

### Final answer:
The solutions are:
\[
x_1 = 2.5 \quad \text{and} \quad x_2 = 1.5
\]

Would you like more details on any step?

### Related Questions:
1. How does the discriminant affect the nature of the roots in a quadratic equation?
2. Can you solve this equation using factoring instead of the quadratic formula?
3. What happens if the discriminant is negative in a quadratic equation?
4. How can you graph the equation \(4x^2 - 16x + 15 = 0\)?
5. How do you derive the quadratic formula?

**Tip:** Always check if a quadratic equation can be factored before using the quadratic formula—it can save time!

Learn how to solve the quadratic equation 4x^2 - 16x + 15 = 0 using the quadratic formula. This detailed step-by-step guide covers key algebraic concepts such as the discriminant and the quadratic formula. Suitable for students in Grades 9-10.

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