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

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

Solve for a

$$a=4x+1+\frac{1}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by a-1.

$$4x^{2}-\left(xa-x\right)+1=0$$

To find the opposite of xa-x, find the opposite of each term.

$$4x^{2}-xa+x+1=0$$

Subtract 4x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-xa+x+1=-4x^{2}$$

Subtract x from both sides.

$$-xa+1=-4x^{2}-x$$

Subtract 1 from both sides.

$$-xa=-4x^{2}-x-1$$

The equation is in standard form.

$$\left(-x\right)a=-4x^{2}-x-1$$

Divide both sides by -x.

$$\frac{\left(-x\right)a}{-x}=\frac{-4x^{2}-x-1}{-x}$$

Dividing by -x undoes the multiplication by -x.

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

Divide -4x^{2}-x-1 by -x.

$$a=4x+1+\frac{1}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{\left(a-5\right)\left(a+3\right)}+a-1}{8}$$

$$x=\frac{-\sqrt{\left(a-5\right)\left(a+3\right)}+a-1}{8}$$

Solve for x

$$x=\frac{\sqrt{\left(a-5\right)\left(a+3\right)}+a-1}{8}$$

$$x=\frac{-\sqrt{\left(a-5\right)\left(a+3\right)}+a-1}{8}\text{, }a\leq -3\text{ or }a\geq 5$$