Solve y=2+frac{sqrt{x}-a}{x}

$$y = 2 + \frac { \sqrt { x } - a } { x }$$

Solve for a (complex solution)

$$a=-xy+2x+\sqrt{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$yx=x\times 2+\sqrt{x}-a$$

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

$$x\times 2+\sqrt{x}-a=yx$$

Subtract x\times 2 from both sides.

$$\sqrt{x}-a=yx-x\times 2$$

Subtract \sqrt{x} from both sides.

$$-a=yx-x\times 2-\sqrt{x}$$

Multiply -1 and 2 to get -2.

$$-a=yx-2x-\sqrt{x}$$

The equation is in standard form.

$$-a=xy-2x-\sqrt{x}$$

Divide both sides by -1.

$$\frac{-a}{-1}=\frac{xy-2x-\sqrt{x}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a=\frac{xy-2x-\sqrt{x}}{-1}$$

Divide yx-2x-\sqrt{x} by -1.

$$a=-xy+2x+\sqrt{x}$$

Solve for a

$$a=-xy+2x+\sqrt{x}$$

$$x>0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$yx=x\times 2+\sqrt{x}-a$$

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

$$x\times 2+\sqrt{x}-a=yx$$

Subtract x\times 2 from both sides.

$$\sqrt{x}-a=yx-x\times 2$$

Subtract \sqrt{x} from both sides.

$$-a=yx-x\times 2-\sqrt{x}$$

Multiply -1 and 2 to get -2.

$$-a=yx-2x-\sqrt{x}$$

The equation is in standard form.

$$-a=xy-2x-\sqrt{x}$$

Divide both sides by -1.

$$\frac{-a}{-1}=\frac{xy-2x-\sqrt{x}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a=\frac{xy-2x-\sqrt{x}}{-1}$$

Divide yx-2x-\sqrt{x} by -1.

$$a=-xy+2x+\sqrt{x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\left(\frac{\sqrt{1+8a-4ay}+1}{2-y}\right)^{2}}{4}\text{, }&arg(\frac{\sqrt{1+8a-4ay}+1}{4-2y})\geq \pi \text{ and }y\neq 2\\x=\frac{\left(\frac{-\sqrt{1+8a-4ay}+1}{2-y}\right)^{2}}{4}\text{, }&a\neq 0\text{ and }y\neq 2\text{ and }arg(\frac{-\sqrt{1+8a-4ay}+1}{4-2y})\geq \pi \\x=a^{2}\text{, }&a\neq 0\text{ and }y=2\text{ and }arg(a)<\pi \end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\left(\frac{\sqrt{1+8a-4ay}+1}{2-y}\right)^{2}}{4}\text{, }&\left(y=\frac{8a+1}{4a}\text{ and }a>0\right)\text{ or }\left(a=0\text{ and }y>2\right)\text{ or }\left(y>2\text{ and }y>\frac{8a+1}{4a}\text{ and }a<0\right)\text{ or }\left(y>2\text{ and }y\leq \frac{8a+1}{4a}\text{ and }a>0\right)\\x=\frac{\left(\frac{-\sqrt{1+8a-4ay}+1}{2-y}\right)^{2}}{4}\text{, }&\left(y\neq 2\text{ and }y<\frac{8a+1}{4a}\text{ and }a>0\right)\text{ or }\left(y>2\text{ and }y\leq \frac{8a+1}{4a}\text{ and }a>0\right)\text{ or }\left(y=\frac{8a+1}{4a}\text{ and }a>0\right)\\x=a^{2}\text{, }&y=2\text{ and }a>0\end{matrix}\right.$$