Solve the following quadratic equation by using the quadratic formula. If needed, submit your answer as a fraction reduced to lowest terms or round your answer to two decimal places

Solution
Solve the following quadratic equation by using the quadratic formula
[tex]3z^2-2z=0[/tex][tex]z=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex][tex]\begin{gathered} 3z^2-2z+0=0 \\ a=3,b=-2,c=0 \end{gathered}[/tex][tex]\begin{gathered} z=\frac{-(-2)\pm\sqrt{(-2)^2-4(3)(0)}}{2(3)} \\ z=\frac{2\pm\sqrt{4}}{6} \\ z=\frac{2\pm2}{6} \\ z=\frac{2+2}{6},\frac{2-2}{6} \\ z=\frac{4}{6},\frac{0}{6} \\ x=\frac{2}{3},0 \end{gathered}[/tex]Therefore the correct answer is
[tex]z=\frac{2}{3},0[/tex]