Solve x*varphiz+7t^2-20sqrt{3}t=8/6

$$x \cdot \varphi z + 7 t ^ { 2 } - 20 \sqrt { 3 } t = 8 / 6$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{21t^{2}-60\sqrt{3}t-4}{3z\phi }\text{, }&z\neq 0\text{ and }\phi \neq 0\\x\in \mathrm{C}\text{, }&\left(t=\frac{10\sqrt{3}}{7}-\frac{4\sqrt{174}}{21}\text{ and }z=0\right)\text{ or }\left(t=\frac{4\sqrt{174}}{21}+\frac{10\sqrt{3}}{7}\text{ and }z=0\right)\text{ or }\left(t=\frac{4\sqrt{174}}{21}+\frac{10\sqrt{3}}{7}\text{ and }\phi =0\text{ and }z\neq 0\right)\text{ or }\left(t=\frac{10\sqrt{3}}{7}-\frac{4\sqrt{174}}{21}\text{ and }\phi =0\text{ and }z\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$x\phi z+7t^{2}-20\sqrt{3}t=\frac{4}{3}$$

Add 20\sqrt{3}t to both sides.

$$x\phi z+7t^{2}=\frac{4}{3}+20\sqrt{3}t$$

Subtract 7t^{2} from both sides.

$$x\phi z=\frac{4}{3}+20\sqrt{3}t-7t^{2}$$

The equation is in standard form.

$$z\phi x=-7t^{2}+20\sqrt{3}t+\frac{4}{3}$$

Divide both sides by \phi z.

$$\frac{z\phi x}{z\phi }=\frac{-7t^{2}+20\sqrt{3}t+\frac{4}{3}}{z\phi }$$

Dividing by \phi z undoes the multiplication by \phi z.

$$x=\frac{-7t^{2}+20\sqrt{3}t+\frac{4}{3}}{z\phi }$$

Divide \frac{4}{3}+20\sqrt{3}t-7t^{2} by \phi z.

$$x=\frac{-21t^{2}+60\sqrt{3}t+4}{3z\phi }$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{21t^{2}-60\sqrt{3}t-4}{3z\phi }\text{, }&z\neq 0\text{ and }\phi \neq 0\\x\in \mathrm{R}\text{, }&\left(t=\frac{10\sqrt{3}}{7}-\frac{4\sqrt{174}}{21}\text{ and }z=0\right)\text{ or }\left(t=\frac{4\sqrt{174}}{21}+\frac{10\sqrt{3}}{7}\text{ and }z=0\right)\text{ or }\left(t=\frac{4\sqrt{174}}{21}+\frac{10\sqrt{3}}{7}\text{ and }\phi =0\text{ and }z\neq 0\right)\text{ or }\left(t=\frac{10\sqrt{3}}{7}-\frac{4\sqrt{174}}{21}\text{ and }\phi =0\text{ and }z\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$x\phi z+7t^{2}-20\sqrt{3}t=\frac{4}{3}$$

Add 20\sqrt{3}t to both sides.

$$x\phi z+7t^{2}=\frac{4}{3}+20\sqrt{3}t$$

Subtract 7t^{2} from both sides.

$$x\phi z=\frac{4}{3}+20\sqrt{3}t-7t^{2}$$

The equation is in standard form.

$$z\phi x=-7t^{2}+20\sqrt{3}t+\frac{4}{3}$$

Divide both sides by \phi z.

$$\frac{z\phi x}{z\phi }=\frac{-7t^{2}+20\sqrt{3}t+\frac{4}{3}}{z\phi }$$

Dividing by \phi z undoes the multiplication by \phi z.

$$x=\frac{-7t^{2}+20\sqrt{3}t+\frac{4}{3}}{z\phi }$$

Divide \frac{4}{3}+20\sqrt{3}t-7t^{2} by \phi z.

$$x=\frac{-21t^{2}+60\sqrt{3}t+4}{3z\phi }$$

Solve for t (complex solution)

$$t=\frac{\sqrt{2784-63xz\phi }}{21}+\frac{10\sqrt{3}}{7}$$

$$t=-\frac{\sqrt{2784-63xz\phi }}{21}+\frac{10\sqrt{3}}{7}$$

Solve for t

$$t=\frac{\sqrt{2784-63xz\phi }}{21}+\frac{10\sqrt{3}}{7}$$

$$t=-\frac{\sqrt{2784-63xz\phi }}{21}+\frac{10\sqrt{3}}{7}\text{, }\left(z\leq 0\text{ or }\phi \leq 0\text{ or }x\leq \frac{928}{21z\phi }\right)\text{ and }\left(x\geq \frac{928}{21z\phi }\text{ or }\phi \leq 0\text{ or }z\geq 0\right)\text{ and }\left(\phi \geq 0\text{ or }x\geq \frac{928}{21z\phi }\text{ or }z\leq 0\right)\text{ and }\left(\phi \geq 0\text{ or }z\geq 0\text{ or }x\leq \frac{928}{21z\phi }\right)$$