Solve delta=1+frac{sqrt{2}}{2}operatorname{vot}-4at^2

$$\delta = 1 + \frac { \sqrt { 2 } } { 2 } \operatorname { vot } - 4 a t ^ { 2 }$$

Solve for a

$$\left\{\begin{matrix}a=\frac{\sqrt{2}otv-2\delta +2}{8t^{2}}\text{, }&t\neq 0\\a\in \mathrm{R}\text{, }&\delta =1\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Express \frac{\sqrt{2}}{2}v as a single fraction.

$$\delta =1+\frac{\sqrt{2}v}{2}ot-4at^{2}$$

Express \frac{\sqrt{2}v}{2}o as a single fraction.

$$\delta =1+\frac{\sqrt{2}vo}{2}t-4at^{2}$$

Express \frac{\sqrt{2}vo}{2}t as a single fraction.

$$\delta =1+\frac{\sqrt{2}vot}{2}-4at^{2}$$

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

$$1+\frac{\sqrt{2}vot}{2}-4at^{2}=\delta$$

Subtract 1 from both sides.

$$\frac{\sqrt{2}vot}{2}-4at^{2}=\delta -1$$

Subtract \frac{\sqrt{2}vot}{2} from both sides.

$$-4at^{2}=\delta -1-\frac{\sqrt{2}vot}{2}$$

Multiply both sides of the equation by 2.

$$-8at^{2}=2\delta -2-\sqrt{2}vot$$

The equation is in standard form.

$$\left(-8t^{2}\right)a=-\sqrt{2}otv+2\delta -2$$

Divide both sides by -8t^{2}.

$$\frac{\left(-8t^{2}\right)a}{-8t^{2}}=\frac{-\sqrt{2}otv+2\delta -2}{-8t^{2}}$$

Dividing by -8t^{2} undoes the multiplication by -8t^{2}.

$$a=\frac{-\sqrt{2}otv+2\delta -2}{-8t^{2}}$$

Divide 2\delta -2-\sqrt{2}vot by -8t^{2}.

$$a=-\frac{-\sqrt{2}otv+2\delta -2}{8t^{2}}$$

Solve for o

$$\left\{\begin{matrix}o=-\frac{\sqrt{2}\left(1-\delta -4at^{2}\right)}{tv}\text{, }&v\neq 0\text{ and }t\neq 0\\o\in \mathrm{R}\text{, }&\left(\delta =1\text{ and }t=0\right)\text{ or }\left(\delta =1-4at^{2}\text{ and }v=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Express \frac{\sqrt{2}}{2}v as a single fraction.

$$\delta =1+\frac{\sqrt{2}v}{2}ot-4at^{2}$$

Express \frac{\sqrt{2}v}{2}o as a single fraction.

$$\delta =1+\frac{\sqrt{2}vo}{2}t-4at^{2}$$

Express \frac{\sqrt{2}vo}{2}t as a single fraction.

$$\delta =1+\frac{\sqrt{2}vot}{2}-4at^{2}$$

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

$$1+\frac{\sqrt{2}vot}{2}-4at^{2}=\delta$$

Add 4at^{2} to both sides.

$$1+\frac{\sqrt{2}vot}{2}=\delta +4at^{2}$$

Subtract 1 from both sides.

$$\frac{\sqrt{2}vot}{2}=\delta +4at^{2}-1$$

Multiply both sides of the equation by 2.

$$\sqrt{2}vot=2\delta +8at^{2}-2$$

The equation is in standard form.

$$\sqrt{2}tvo=8at^{2}+2\delta -2$$

Divide both sides by \sqrt{2}vt.

$$\frac{\sqrt{2}tvo}{\sqrt{2}tv}=\frac{8at^{2}+2\delta -2}{\sqrt{2}tv}$$

Dividing by \sqrt{2}vt undoes the multiplication by \sqrt{2}vt.

$$o=\frac{8at^{2}+2\delta -2}{\sqrt{2}tv}$$

Divide 2\delta +8t^{2}a-2 by \sqrt{2}vt.

$$o=\frac{\sqrt{2}\left(4at^{2}+\delta -1\right)}{tv}$$