Multiply $\sqrt{t}$ and $\sqrt{t}$ to get $\left(\sqrt{t}\right)^{2}$.
$$\left(\sqrt{t}\right)^{2}=3t^{2}i+t$$
Calculate $\sqrt{t}$ to the power of $2$ and get $t$.
$$t=3t^{2}i+t$$
Multiply $3$ and $i$ to get $3i$.
$$t=3it^{2}+t$$
Subtract $3it^{2}$ from both sides.
$$t-3it^{2}=t$$
Subtract $t$ from both sides.
$$t-3it^{2}-t=0$$
Combine $t$ and $-t$ to get $0$.
$$-3it^{2}=0$$
Divide both sides by $-3i$. Zero divided by any non-zero number gives zero.
$$t^{2}=0$$
The equation is now solved. Solutions are the same.
$$t=0$$
Steps Using the Quadratic Formula
Multiply $\sqrt{t}$ and $\sqrt{t}$ to get $\left(\sqrt{t}\right)^{2}$.
$$\left(\sqrt{t}\right)^{2}=3t^{2}i+t$$
Calculate $\sqrt{t}$ to the power of $2$ and get $t$.
$$t=3t^{2}i+t$$
Multiply $3$ and $i$ to get $3i$.
$$t=3it^{2}+t$$
Subtract $3it^{2}$ from both sides.
$$t-3it^{2}=t$$
Subtract $t$ from both sides.
$$t-3it^{2}-t=0$$
Combine $t$ and $-t$ to get $0$.
$$-3it^{2}=0$$
Divide both sides by $-3i$. Zero divided by any non-zero number gives zero.
$$t^{2}=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $0$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
