x^2-5/6+1/6=0

To solve the equation \( x^2 - \frac{5}{6} + \frac{1}{6} = 0 \), we first simplify the expression:

1. Combine the fractions: \[ -\frac{5}{6} + \frac{1}{6} = -\frac{5 - 1}{6} = -\frac{4}{6} = -\frac{2}{3} \]

2. Rewrite the equation: \[ x^2 - \frac{2}{3} = 0 \]

3. Move \(-\frac{2}{3}\) to the other side: \[ x^2 = \frac{2}{3} \]

4. Take the square root of both sides: \[ x = \pm \sqrt{\frac{2}{3}} \]

5. This can also be simplified by multiplying the numerator and the denominator by \(\sqrt{3}\): \[ x = \pm \frac{\sqrt{6}}{3} \]

Thus, the solutions to the equation \( x^2 - \frac{5}{6} + \frac{1}{6} = 0 \) are: \[ x = \frac{\sqrt{6}}{3} \quad \text{and} \quad x = -\frac{\sqrt{6}}{3} \]