Answer
{$0,-\frac{10}{3}$}
Work Step by Step
Step 1: $3x^{2}=-10x$ can also be written as $3x^{2}+10x+0=0$. Comparing $3x^{2}+10x+0=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$, we obtain: $a=3$, $b=10$ and $c=0$
Step 2: The quadratic formula is: $x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$
Step 3: Substituting the values of a, b and c in the formula: $x=\frac{-(10) \pm \sqrt {(10)^{2}-4(3)(0)}}{2(3)}$
Step 4: $x=\frac{-10 \pm \sqrt {100-0}}{6}$
Step 5: $x=\frac{-10 \pm \sqrt {100}}{6}$
Step 6: $x=\frac{-10 \pm 10}{6}$
Step 7: $x=\frac{-10+10}{6}$ or $x=\frac{-10-10}{6}$
Step 8: $x=\frac{0}{6}$ or $x=\frac{-20}{6}$
Step 9: $x=0$ or $x=-\frac{10}{3}$
Step 10: Therefore, the solution set is {$0,-\frac{10}{3}$}.
