Solve 2ax^2+(2-a)x-1=0

$$2 a x ^ { 2 } + ( 2 - a ) x - 1 = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2-a by x.

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

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

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

Add 1 to both sides.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by 2x^{2}-x.

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

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

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

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

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

Solve for a

$$\left\{\begin{matrix}a=-\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2-a by x.

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

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

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

Add 1 to both sides.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by 2x^{2}-x.

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

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

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

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

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

Solve for x

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