Solve W=I^2Rt

$$W = I ^ { 2 } R t$$

Solve for R (complex solution)

$$\left\{\begin{matrix}R=\frac{W}{tI^{2}}\text{, }&t\neq 0\text{ and }I\neq 0\\R\in \mathrm{C}\text{, }&\left(t=0\text{ or }I=0\right)\text{ and }W=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$I^{2}Rt=W$$

The equation is in standard form.

$$tI^{2}R=W$$

Divide both sides by I^{2}t.

$$\frac{tI^{2}R}{tI^{2}}=\frac{W}{tI^{2}}$$

Dividing by I^{2}t undoes the multiplication by I^{2}t.

$$R=\frac{W}{tI^{2}}$$

Solve for R

$$\left\{\begin{matrix}R=\frac{W}{tI^{2}}\text{, }&t\neq 0\text{ and }I\neq 0\\R\in \mathrm{R}\text{, }&\left(t=0\text{ or }I=0\right)\text{ and }W=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$I^{2}Rt=W$$

The equation is in standard form.

$$tI^{2}R=W$$

Divide both sides by I^{2}t.

$$\frac{tI^{2}R}{tI^{2}}=\frac{W}{tI^{2}}$$

Dividing by I^{2}t undoes the multiplication by I^{2}t.

$$R=\frac{W}{tI^{2}}$$

Solve for I (complex solution)

$$\left\{\begin{matrix}I=-R^{-\frac{1}{2}}t^{-\frac{1}{2}}\sqrt{W}\text{; }I=R^{-\frac{1}{2}}t^{-\frac{1}{2}}\sqrt{W}\text{, }&t\neq 0\text{ and }R\neq 0\\I\in \mathrm{C}\text{, }&\left(t=0\text{ or }R=0\right)\text{ and }W=0\end{matrix}\right.$$

Solve for I

$$\left\{\begin{matrix}I=\sqrt{\frac{W}{Rt}}\text{; }I=-\sqrt{\frac{W}{Rt}}\text{, }&\left(W\leq 0\text{ and }R<0\text{ and }t>0\right)\text{ or }\left(W\geq 0\text{ and }R>0\text{ and }t>0\right)\text{ or }\left(W\leq 0\text{ and }t<0\text{ and }R>0\right)\text{ or }\left(W\geq 0\text{ and }t<0\text{ and }R<0\right)\\I\in \mathrm{R}\text{, }&\left(t=0\text{ or }R=0\right)\text{ and }W=0\end{matrix}\right.$$