$-3 t^{2}+t=0$

Step 1 ：Given the quadratic equation \(-3t^2 + t = 0\), we can use the quadratic formula to find the solutions for t: \(t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Step 2 ：Plugging the values a = -3, b = 1, and c = 0 into the formula, we get the solutions for t: \(t_1 = 0\) and \(t_2 = \frac{1}{3}\)

Step 3 ：\boxed{\text{Final Answer: The solutions for t are 0 and }\frac{1}{3}}