The problem asks us to find the solution set of the quadratic equation $2x^2 - 7x + 1 = 0$ using the quadratic formula.

1. Problem Description

The problem asks us to find the solution set of the quadratic equation $2x^2 - 7x + 1 = 0$ using the quadratic formula.

2. Solution Steps

The quadratic formula is given by

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

for the quadratic equation $ax^2 + bx + c = 0$.

In the given equation $2x^2 - 7x + 1 = 0$, we have $a = 2$, $b = -7$, and $c = 1$.

Substituting these values into the quadratic formula, we get

$$x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(2)(1)}}{2(2)}$$

$$x = \frac{7 \pm \sqrt{49 - 8}}{4}$$

$$x = \frac{7 \pm \sqrt{41}}{4}$$

Thus, the two solutions are $x_1 = \frac{7 + \sqrt{41}}{4}$ and $x_2 = \frac{7 - \sqrt{41}}{4}$.

3. Final Answer

The solution set is $\{\frac{7 + \sqrt{41}}{4}, \frac{7 - \sqrt{41}}{4}\}$.