Solve Deltax=1/2alphat^2

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

Solve for x (complex solution)

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

Steps for Solving Linear Equation

The equation is in standard form.

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

Divide both sides by \Delta .

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

Dividing by \Delta undoes the multiplication by \Delta .

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

Solve for x

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

Steps for Solving Linear Equation

The equation is in standard form.

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

Divide both sides by \Delta .

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

Dividing by \Delta undoes the multiplication by \Delta .

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

Solve for t (complex solution)

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

Solve for t

$$\left\{\begin{matrix}t=\sqrt{\frac{2x\Delta }{\alpha }}\text{; }t=-\sqrt{\frac{2x\Delta }{\alpha }}\text{, }&\left(x\leq 0\text{ and }\Delta \geq 0\text{ and }\alpha <0\right)\text{ or }\left(x\geq 0\text{ and }\Delta \geq 0\text{ and }\alpha >0\right)\text{ or }\left(\Delta \leq 0\text{ and }x\leq 0\text{ and }\alpha >0\right)\text{ or }\left(\Delta \leq 0\text{ and }x\geq 0\text{ and }\alpha <0\right)\\t\in \mathrm{R}\text{, }&\left(\Delta =0\text{ or }x=0\right)\text{ and }\alpha =0\end{matrix}\right.$$