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

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

Solve for a

$$a=-x\left(x+1\right)$$

$$x\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x+1.

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

Use the distributive property to multiply x by 2x+1.

$$2x^{2}+x=x^{2}-a$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-a=2x^{2}+x$$

Subtract x^{2} from both sides.

$$-a=2x^{2}+x-x^{2}$$

Combine 2x^{2} and -x^{2} to get x^{2}.

$$-a=x^{2}+x$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide x\left(1+x\right) by -1.

$$a=-x\left(x+1\right)$$

Solve for x (complex solution)

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

$$x=\frac{-\sqrt{1-4a}-1}{2}\text{, }a\neq \frac{1}{4}$$

Solve for x

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

$$x=\frac{-\sqrt{1-4a}-1}{2}\text{, }a<\frac{1}{4}$$