The problem is to solve the quadratic equation $2x^2 - 7x + 1 = 0$.

1. Problem Description

The problem is to solve the quadratic equation $2x^2 - 7x + 1 = 0$.

2. Solution Steps

We will use the quadratic formula to solve for $x$. The quadratic formula is given by:

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

In our equation, $2x^2 - 7x + 1 = 0$, we have $a = 2$, $b = -7$, and $c = 1$. Substituting these values into the quadratic formula, we get:

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

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

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

Therefore, the two solutions are:

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

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

3. Final Answer

The solutions to the equation are $x = \frac{7 + \sqrt{41}}{4}$ and $x = \frac{7 - \sqrt{41}}{4}$.