Solve ab-vt^2=m

$$a b - v t ^ { 2 } = m$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{m+vt^{2}}{b}\text{, }&b\neq 0\\a\in \mathrm{C}\text{, }&m=-vt^{2}\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add vt^{2} to both sides.

$$ab=m+vt^{2}$$

The equation is in standard form.

$$ba=m+vt^{2}$$

Divide both sides by b.

$$\frac{ba}{b}=\frac{m+vt^{2}}{b}$$

Dividing by b undoes the multiplication by b.

$$a=\frac{m+vt^{2}}{b}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{m+vt^{2}}{a}\text{, }&a\neq 0\\b\in \mathrm{C}\text{, }&m=-vt^{2}\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add vt^{2} to both sides.

$$ab=m+vt^{2}$$

Divide both sides by a.

$$\frac{ab}{a}=\frac{m+vt^{2}}{a}$$

Dividing by a undoes the multiplication by a.

$$b=\frac{m+vt^{2}}{a}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{m+vt^{2}}{b}\text{, }&b\neq 0\\a\in \mathrm{R}\text{, }&m=-vt^{2}\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add vt^{2} to both sides.

$$ab=m+vt^{2}$$

The equation is in standard form.

$$ba=m+vt^{2}$$

Divide both sides by b.

$$\frac{ba}{b}=\frac{m+vt^{2}}{b}$$

Dividing by b undoes the multiplication by b.

$$a=\frac{m+vt^{2}}{b}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{m+vt^{2}}{a}\text{, }&a\neq 0\\b\in \mathrm{R}\text{, }&m=-vt^{2}\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add vt^{2} to both sides.

$$ab=m+vt^{2}$$

Divide both sides by a.

$$\frac{ab}{a}=\frac{m+vt^{2}}{a}$$

Dividing by a undoes the multiplication by a.

$$b=\frac{m+vt^{2}}{a}$$