Solve (D)^2=(sqrt{WL/15B})^2

$$( D ) ^ { 2 } = ( \sqrt { \frac { W L } { 15 B } } ) ^ { 2 }$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B\neq 0\text{, }&\left(W=0\text{ or }L=0\right)\text{ and }D=0\\B=\frac{LW}{15D^{2}}\text{, }&\left(|\frac{arg(D^{2})}{2}-arg(D)|<\pi \text{ or }arg(D)\geq \pi \right)\text{ and }L\neq 0\text{ and }W\neq 0\text{ and }D\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate \sqrt{\frac{WL}{15B}} to the power of 2 and get \frac{WL}{15B}.

$$D^{2}=\frac{WL}{15B}$$

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

$$\frac{WL}{15B}=D^{2}$$

Variable B cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 15B.

$$WL=15BD^{2}$$

Reorder the terms.

$$LW=15BD^{2}$$

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

$$15BD^{2}=LW$$

The equation is in standard form.

$$15D^{2}B=LW$$

Divide both sides by 15D^{2}.

$$\frac{15D^{2}B}{15D^{2}}=\frac{LW}{15D^{2}}$$

Dividing by 15D^{2} undoes the multiplication by 15D^{2}.

$$B=\frac{LW}{15D^{2}}$$

Variable B cannot be equal to 0.

$$B=\frac{LW}{15D^{2}}\text{, }B\neq 0$$

Solve for B

$$\left\{\begin{matrix}B\neq 0\text{, }&\left(L=0\text{ or }W=0\right)\text{ and }D=0\\B=\frac{LW}{15D^{2}}\text{, }&L\neq 0\text{ and }W\neq 0\text{ and }D\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate \sqrt{\frac{WL}{15B}} to the power of 2 and get \frac{WL}{15B}.

$$D^{2}=\frac{WL}{15B}$$

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

$$\frac{WL}{15B}=D^{2}$$

Variable B cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 15B.

$$WL=15BD^{2}$$

Reorder the terms.

$$LW=15BD^{2}$$

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

$$15BD^{2}=LW$$

The equation is in standard form.

$$15D^{2}B=LW$$

Divide both sides by 15D^{2}.

$$\frac{15D^{2}B}{15D^{2}}=\frac{LW}{15D^{2}}$$

Dividing by 15D^{2} undoes the multiplication by 15D^{2}.

$$B=\frac{LW}{15D^{2}}$$

Variable B cannot be equal to 0.

$$B=\frac{LW}{15D^{2}}\text{, }B\neq 0$$

Solve for D (complex solution)

$$D=-\frac{B^{-\frac{1}{2}}\sqrt{L}\sqrt{15W}}{15}$$

$$D=\frac{B^{-\frac{1}{2}}\sqrt{L}\sqrt{15W}}{15}\text{, }B\neq 0$$

Solve for D

$$D=\frac{\sqrt{\frac{15LW}{B}}}{15}$$

$$D=-\frac{\sqrt{\frac{15LW}{B}}}{15}\text{, }\left(L\leq 0\text{ and }W\leq 0\text{ and }B>0\right)\text{ or }\left(W\geq 0\text{ and }L\geq 0\text{ and }B>0\right)\text{ or }\left(W\leq 0\text{ and }L\geq 0\text{ and }B<0\right)\text{ or }\left(L\leq 0\text{ and }W\geq 0\text{ and }B<0\right)$$