Solve 2ax-1/x=0

$$2 a x - \frac { 1 } { x } = 0$$

Solve for a

$$a=\frac{1}{2x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$2axx-1=0$$

Multiply x and x to get x^{2}.

$$2ax^{2}-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$2ax^{2}=1$$

The equation is in standard form.

$$2x^{2}a=1$$

Divide both sides by 2x^{2}.

$$\frac{2x^{2}a}{2x^{2}}=\frac{1}{2x^{2}}$$

Dividing by 2x^{2} undoes the multiplication by 2x^{2}.

$$a=\frac{1}{2x^{2}}$$

Solve for x (complex solution)

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

$$x=\frac{\sqrt{2}a^{-\frac{1}{2}}}{2}\text{, }a\neq 0$$

Solve for x

$$x=\frac{\sqrt{\frac{2}{a}}}{2}$$

$$x=-\frac{\sqrt{\frac{2}{a}}}{2}\text{, }a>0$$