Solve 1/x-ax-2=0

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

Solve for a

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

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$1-axx+x\left(-2\right)=0$$

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

$$1-ax^{2}+x\left(-2\right)=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-ax^{2}+x\left(-2\right)=-1$$

Subtract x\left(-2\right) from both sides.

$$-ax^{2}=-1-x\left(-2\right)$$

Multiply -1 and -2 to get 2.

$$-ax^{2}=-1+2x$$

The equation is in standard form.

$$\left(-x^{2}\right)a=2x-1$$

Divide both sides by -x^{2}.

$$\frac{\left(-x^{2}\right)a}{-x^{2}}=\frac{2x-1}{-x^{2}}$$

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

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

Divide -1+2x by -x^{2}.

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{a+1}+1}{a}\text{; }x=\frac{\sqrt{a+1}-1}{a}\text{, }&a\neq 0\\x=\frac{1}{2}\text{, }&a=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{a+1}+1}{a}\text{; }x=\frac{\sqrt{a+1}-1}{a}\text{, }&a\neq 0\text{ and }a\geq -1\\x=\frac{1}{2}\text{, }&a=0\end{matrix}\right.$$