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.