Solve 1/2sigma+partialV/Sd=0

$$\frac { 1 } { 2 } \sigma + \frac { \partial V } { S d } = 0$$

Solve for S

$$\left\{\begin{matrix}S=-\frac{2V∂}{d\sigma }\text{, }&∂\neq 0\text{ and }V\neq 0\text{ and }d\neq 0\text{ and }\sigma \neq 0\\S\neq 0\text{, }&\left(∂=0\text{ or }V=0\right)\text{ and }\sigma =0\text{ and }d\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable S cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2Sd, the least common multiple of 2,Sd.

$$\frac{1}{2}\sigma \times 2Sd+2∂V=0$$

Multiply \frac{1}{2} and 2 to get 1.

$$\sigma Sd+2∂V=0$$

Subtract 2∂V from both sides. Anything subtracted from zero gives its negation.

$$\sigma Sd=-2∂V$$

The equation is in standard form.

$$d\sigma S=-2V∂$$

Divide both sides by \sigma d.

$$\frac{d\sigma S}{d\sigma }=-\frac{2V∂}{d\sigma }$$

Dividing by \sigma d undoes the multiplication by \sigma d.

$$S=-\frac{2V∂}{d\sigma }$$

Variable S cannot be equal to 0.

$$S=-\frac{2V∂}{d\sigma }\text{, }S\neq 0$$

Solve for V

$$\left\{\begin{matrix}V=-\frac{Sd\sigma }{2∂}\text{, }&∂\neq 0\text{ and }S\neq 0\text{ and }d\neq 0\\V\in \mathrm{R}\text{, }&\sigma =0\text{ and }∂=0\text{ and }S\neq 0\text{ and }d\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2Sd, the least common multiple of 2,Sd.

$$\frac{1}{2}\sigma \times 2Sd+2∂V=0$$

Multiply \frac{1}{2} and 2 to get 1.

$$\sigma Sd+2∂V=0$$

Subtract \sigma Sd from both sides. Anything subtracted from zero gives its negation.

$$2∂V=-\sigma Sd$$

Reorder the terms.

$$2V∂=-Sd\sigma$$

The equation is in standard form.

$$2∂V=-Sd\sigma$$

Divide both sides by 2∂.

$$\frac{2∂V}{2∂}=-\frac{Sd\sigma }{2∂}$$

Dividing by 2∂ undoes the multiplication by 2∂.

$$V=-\frac{Sd\sigma }{2∂}$$