Solve (a-1)x^2-x+1/4=0

$$( a - 1 ) x ^ { 2 } - x + \frac { 1 } { 4 } = 0$$

Solve for a

$$a=1+\frac{1}{x}-\frac{1}{4x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply a-1 by x^{2}.

$$ax^{2}-x^{2}-x+\frac{1}{4}=0$$

Add x^{2} to both sides. Anything plus zero gives itself.

$$ax^{2}-x+\frac{1}{4}=x^{2}$$

Add x to both sides.

$$ax^{2}+\frac{1}{4}=x^{2}+x$$

Subtract \frac{1}{4} from both sides.

$$ax^{2}=x^{2}+x-\frac{1}{4}$$

The equation is in standard form.

$$x^{2}a=x^{2}+x-\frac{1}{4}$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{x^{2}+x-\frac{1}{4}}{x^{2}}$$

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

$$a=\frac{x^{2}+x-\frac{1}{4}}{x^{2}}$$

Divide x^{2}+x-\frac{1}{4} by x^{2}.

$$a=1+\frac{x-\frac{1}{4}}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{2-a}+1}{2\left(a-1\right)}\text{; }x=\frac{-\sqrt{2-a}+1}{2\left(a-1\right)}\text{, }&a\neq 1\\x=\frac{1}{4}\text{, }&a=1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{2-a}+1}{2\left(a-1\right)}\text{; }x=\frac{-\sqrt{2-a}+1}{2\left(a-1\right)}\text{, }&a\neq 1\text{ and }a\leq 2\\x=\frac{1}{4}\text{, }&a=1\end{matrix}\right.$$