Solve Deltavartheta=DeltaV/V_{0*3alpha}

$$\Delta \vartheta = \frac { \Delta V } { V _ { 0 } \cdot 3 \alpha }$$

Solve for V

$$\left\{\begin{matrix}V=3V_{0}\alpha ϑ\text{, }&\alpha \neq 0\text{ and }V_{0}\neq 0\\V\in \mathrm{R}\text{, }&\Delta =0\text{ and }\alpha \neq 0\text{ and }V_{0}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3V_{0}\alpha .

$$\Delta ϑ\times 3V_{0}\alpha =\Delta V$$

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

$$\Delta V=\Delta ϑ\times 3V_{0}\alpha$$

The equation is in standard form.

$$\Delta V=3V_{0}\Delta \alpha ϑ$$

Divide both sides by \Delta .

$$\frac{\Delta V}{\Delta }=\frac{3V_{0}\Delta \alpha ϑ}{\Delta }$$

Dividing by \Delta undoes the multiplication by \Delta .

$$V=\frac{3V_{0}\Delta \alpha ϑ}{\Delta }$$

Divide 3\Delta ϑV_{0}\alpha by \Delta .

$$V=3V_{0}\alpha ϑ$$

Solve for V_0

$$\left\{\begin{matrix}V_{0}=\frac{V}{3\alpha ϑ}\text{, }&V\neq 0\text{ and }\alpha \neq 0\text{ and }ϑ\neq 0\\V_{0}\neq 0\text{, }&\left(\Delta =0\text{ and }\alpha \neq 0\right)\text{ or }\left(ϑ=0\text{ and }V=0\text{ and }\alpha \neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable V_{0} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3V_{0}\alpha .

$$\Delta ϑ\times 3V_{0}\alpha =\Delta V$$

Reorder the terms.

$$3V_{0}\Delta \alpha ϑ=V\Delta$$

The equation is in standard form.

$$3\Delta \alpha ϑV_{0}=V\Delta$$

Divide both sides by 3\Delta \alpha ϑ.

$$\frac{3\Delta \alpha ϑV_{0}}{3\Delta \alpha ϑ}=\frac{V\Delta }{3\Delta \alpha ϑ}$$

Dividing by 3\Delta \alpha ϑ undoes the multiplication by 3\Delta \alpha ϑ.

$$V_{0}=\frac{V\Delta }{3\Delta \alpha ϑ}$$

Divide \Delta V by 3\Delta \alpha ϑ.

$$V_{0}=\frac{V}{3\alpha ϑ}$$

Variable V_{0} cannot be equal to 0.

$$V_{0}=\frac{V}{3\alpha ϑ}\text{, }V_{0}\neq 0$$