Solve Deltax=1/qalphat^2

$$\Delta x = \frac { 1 } { q } \alpha t ^ { 2 }$$

Solve for q

$$\left\{\begin{matrix}q=\frac{\alpha t^{2}}{x\Delta }\text{, }&t\neq 0\text{ and }\alpha \neq 0\text{ and }x\neq 0\text{ and }\Delta \neq 0\\q\neq 0\text{, }&\left(\Delta =0\text{ and }t=0\right)\text{ or }\left(x=0\text{ and }t=0\right)\text{ or }\left(x=0\text{ and }\alpha =0\text{ and }t\neq 0\right)\text{ or }\left(\Delta =0\text{ and }\alpha =0\text{ and }t\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\Delta xq=1\alpha t^{2}$$

Reorder the terms.

$$qx\Delta =\alpha t^{2}$$

The equation is in standard form.

$$x\Delta q=\alpha t^{2}$$

Divide both sides by \Delta x.

$$\frac{x\Delta q}{x\Delta }=\frac{\alpha t^{2}}{x\Delta }$$

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

$$q=\frac{\alpha t^{2}}{x\Delta }$$

Variable q cannot be equal to 0.

$$q=\frac{\alpha t^{2}}{x\Delta }\text{, }q\neq 0$$

Solve for t (complex solution)

$$\left\{\begin{matrix}t=-\alpha ^{-\frac{1}{2}}\sqrt{q}\sqrt{x}\sqrt{\Delta }\text{; }t=\alpha ^{-\frac{1}{2}}\sqrt{q}\sqrt{x}\sqrt{\Delta }\text{, }&q\neq 0\text{ and }\alpha \neq 0\\t\in \mathrm{C}\text{, }&\left(x=0\text{ or }\Delta =0\right)\text{ and }\alpha =0\text{ and }q\neq 0\end{matrix}\right.$$