Mathematics

Problem

\frac{1}{2}x^2 - \frac{1}{6}x - \frac{1}{3} = 0

What are the solutions to the equation above? A.

x=1

and

x=-\frac{2}{3}

x = \frac{1}{6} - \sqrt{\frac{23}{36}}

and

x = \frac{1}{6} + \sqrt{\frac{23}{36}}

x=2

and

x=-\frac{4}{3}

x = \frac{1}{6} - \sqrt{-\frac{23}{36}}

and

x = \frac{1}{6} + \sqrt{-\frac{23}{36}}