Solve BD^2=7AC

$$B D ^ { 2 } = 7 A C$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=\frac{BD^{2}}{7C}\text{, }&C\neq 0\\A\in \mathrm{C}\text{, }&\left(B=0\text{ or }D=0\right)\text{ and }C=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$7AC=BD^{2}$$

The equation is in standard form.

$$7CA=BD^{2}$$

Divide both sides by 7C.

$$\frac{7CA}{7C}=\frac{BD^{2}}{7C}$$

Dividing by 7C undoes the multiplication by 7C.

$$A=\frac{BD^{2}}{7C}$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=\frac{7AC}{D^{2}}\text{, }&D\neq 0\\B\in \mathrm{C}\text{, }&\left(A=0\text{ or }C=0\right)\text{ and }D=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$D^{2}B=7AC$$

Divide both sides by D^{2}.

$$\frac{D^{2}B}{D^{2}}=\frac{7AC}{D^{2}}$$

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

$$B=\frac{7AC}{D^{2}}$$

Solve for A

$$\left\{\begin{matrix}A=\frac{BD^{2}}{7C}\text{, }&C\neq 0\\A\in \mathrm{R}\text{, }&\left(B=0\text{ or }D=0\right)\text{ and }C=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$7AC=BD^{2}$$

The equation is in standard form.

$$7CA=BD^{2}$$

Divide both sides by 7C.

$$\frac{7CA}{7C}=\frac{BD^{2}}{7C}$$

Dividing by 7C undoes the multiplication by 7C.

$$A=\frac{BD^{2}}{7C}$$

Solve for B

$$\left\{\begin{matrix}B=\frac{7AC}{D^{2}}\text{, }&D\neq 0\\B\in \mathrm{R}\text{, }&\left(A=0\text{ or }C=0\right)\text{ and }D=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$D^{2}B=7AC$$

Divide both sides by D^{2}.

$$\frac{D^{2}B}{D^{2}}=\frac{7AC}{D^{2}}$$

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

$$B=\frac{7AC}{D^{2}}$$