3 x2 − 6x + 2 = 0

1. Given quadratic equation: 3x^2 - 6x + 2 = 0

2. Identify coefficients:
a = 3
b = -6
c = 2

3. Find the discriminant:
\Delta = b^2 - 4ac
\Delta = (-6)^2 - 4 \cdot 3 \cdot 2
\Delta = 36 - 24
\Delta = 12

4. Apply the quadratic formula:
x = \frac{-b \pm \sqrt{\Delta}}{2a}

5. Substitute the coefficients and discriminant:
x = \frac{-(-6) \pm \sqrt{12}}{2 \cdot 3}
x = \frac{6 \pm 2\sqrt{3}}{6}
x = 1 \pm \frac{\sqrt{3}}{3}

6. Final answers:
x_1 = 1 + \frac{\sqrt{3}}{3}
x_2 = 1 - \frac{\sqrt{3}}{3}