It seems like you're working with a quadratic equation. The equation you've provided appears to be:

\[ 2x^2 - 6x + 1 = 0 \]

To solve this quadratic equation, you can use the quadratic formula, which is:

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

In this equation, \( a = 2 \), \( b = -6 \), and \( c = 1 \).

Plug these values into the quadratic formula:

\[ x = \frac{{-(-6) \pm \sqrt{{(-6)^2 - 4 \cdot 2 \cdot 1}}}}{2 \cdot 2} \]

\[ x = \frac}}{4} \]

\[ x = \frac}{4} \]

Simplify \(\sqrt{28}\):

\[ \sqrt{28} = \sqrt{4 \cdot 7} = 2\sqrt{7} \]

Substitute back into the equation:

\[ x = \frac}{4} \]

Divide all terms in the numerator by 2:

\[ x = \frac}{2} \]

Therefore, the solutions to the quadratic equation \( 2x^2 - 6x + 1 = 0 \) are:

\[ x = \frac{3 + \sqrt{7}}{2} \quad \text{and} \quad x = \frac{3 - \sqrt{7}}{2} \]