x^2-4x+2=0

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

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

where \( a = 1 \), \( b = -4 \), and \( c = 2 \).

Step-by-step solution:

1. Identify coefficients: \[ a = 1, \quad b = -4, \quad c = 2 \]

2. Calculate the discriminant: \[ D = b^2 - 4ac = (-4)^2 - 4 \times 1 \times 2 = 16 - 8 = 8 \]

3. Compute the square root of the discriminant: \[ \sqrt{D} = \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \]

4. Apply the quadratic formula: \[ x = \frac{-(-4) \pm 2\sqrt{2}}{2 \times 1} = \frac{4 \pm 2\sqrt{2}}{2} \]

5. Simplify: \[ x = 2 \pm \sqrt{2} \]

Final answer:

\[ \boxed{ x = 2 + \sqrt{2} \quad \text{or} \quad x = 2 - \sqrt{2} } \]

These are the solutions to the quadratic equation.