Solve P=sqrt{3}*u*I*cosvarphi

$$P = \sqrt { 3 } \cdot u \cdot I \cdot \cos \varphi$$

Solve for I

$$\left\{\begin{matrix}I=\frac{\sqrt{3}P}{3u\cos(\phi )}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\phi =\pi n_{1}+\frac{\pi }{2}\text{ and }u\neq 0\\I\in \mathrm{R}\text{, }&\left(u=0\text{ or }\exists n_{1}\in \mathrm{Z}\text{ : }\phi =\pi n_{1}+\frac{\pi }{2}\right)\text{ and }P=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\sqrt{3}uI\cos(\phi )=P$$

The equation is in standard form.

$$\sqrt{3}u\cos(\phi )I=P$$

Divide both sides by \sqrt{3}u\cos(\phi ).

$$\frac{\sqrt{3}u\cos(\phi )I}{\sqrt{3}u\cos(\phi )}=\frac{P}{\sqrt{3}u\cos(\phi )}$$

Dividing by \sqrt{3}u\cos(\phi ) undoes the multiplication by \sqrt{3}u\cos(\phi ).

$$I=\frac{P}{\sqrt{3}u\cos(\phi )}$$

Divide P by \sqrt{3}u\cos(\phi ).

$$I=\frac{\sqrt{3}P}{3u\cos(\phi )}$$

Solve for P

$$P=\sqrt{3}Iu\cos(\phi )$$