Solve -DeltaL/L_{0}=aDeltaT

$$- \frac { \Delta L } { L _ { 0 } } = a \Delta T$$

Solve for L

$$\left\{\begin{matrix}L=-L_{0}Ta\text{, }&L_{0}\neq 0\\L\in \mathrm{R}\text{, }&\Delta =0\text{ and }L_{0}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by L_{0}.

$$-\Delta L=a\Delta TL_{0}$$

Reorder the terms.

$$-L\Delta =L_{0}Ta\Delta$$

The equation is in standard form.

$$\left(-\Delta \right)L=L_{0}Ta\Delta$$

Divide both sides by -\Delta .

$$\frac{\left(-\Delta \right)L}{-\Delta }=\frac{L_{0}Ta\Delta }{-\Delta }$$

Dividing by -\Delta undoes the multiplication by -\Delta .

$$L=\frac{L_{0}Ta\Delta }{-\Delta }$$

Divide L_{0}Ta\Delta by -\Delta .

$$L=-L_{0}Ta$$

Solve for L_0

$$\left\{\begin{matrix}L_{0}=-\frac{L}{Ta}\text{, }&L\neq 0\text{ and }T\neq 0\text{ and }a\neq 0\\L_{0}\neq 0\text{, }&\Delta =0\text{ or }\left(a=0\text{ and }L=0\right)\text{ or }\left(T=0\text{ and }L=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-\Delta L=a\Delta TL_{0}$$

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

$$a\Delta TL_{0}=-\Delta L$$

Reorder the terms.

$$L_{0}Ta\Delta =-L\Delta$$

The equation is in standard form.

$$Ta\Delta L_{0}=-L\Delta$$

Divide both sides by a\Delta T.

$$\frac{Ta\Delta L_{0}}{Ta\Delta }=-\frac{L\Delta }{Ta\Delta }$$

Dividing by a\Delta T undoes the multiplication by a\Delta T.

$$L_{0}=-\frac{L\Delta }{Ta\Delta }$$

Divide -L\Delta by a\Delta T.

$$L_{0}=-\frac{L}{Ta}$$

Variable L_{0} cannot be equal to 0.

$$L_{0}=-\frac{L}{Ta}\text{, }L_{0}\neq 0$$