Solve this equation for $t$

Question

I am having trouble solving this equation for $t$ ($s$ is just a paremeter): $$s = t+\frac{t^3}{3}$$

Answer 1

Hint: The number of a real solutions for the equation $x^3+3px+2q=0$ is in relation to the sign of discriminant $D=q^2+p^3$.

Above equation will have $3$ real distinct solutions if $D<0$.

Above equation will have $1$ real solution ($1$ real and $2$ complex roots) if $D>0$.

For $D=0$, above equation will have $1$ real solution ($1$ real root with multiplicity three) in the case $p = q = 0$; or $2$ real solutions (a single and a double real root) in the case $p^3=-q^2 \neq 0$.