Solve x^2-k/2x=2p

$$x ^ { 2 } - \frac { k } { 2 } x = 2 p$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=2x-\frac{4p}{x}\text{, }&x\neq 0\\k\in \mathrm{C}\text{, }&p=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2x^{2}-kx=4p$$

Subtract 2x^{2} from both sides.

$$-kx=4p-2x^{2}$$

The equation is in standard form.

$$\left(-x\right)k=4p-2x^{2}$$

Divide both sides by -x.

$$\frac{\left(-x\right)k}{-x}=\frac{4p-2x^{2}}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$k=\frac{4p-2x^{2}}{-x}$$

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

$$k=2x-\frac{4p}{x}$$

Solve for k

$$\left\{\begin{matrix}k=2x-\frac{4p}{x}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&p=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2x^{2}-kx=4p$$

Subtract 2x^{2} from both sides.

$$-kx=4p-2x^{2}$$

The equation is in standard form.

$$\left(-x\right)k=4p-2x^{2}$$

Divide both sides by -x.

$$\frac{\left(-x\right)k}{-x}=\frac{4p-2x^{2}}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$k=\frac{4p-2x^{2}}{-x}$$

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

$$k=2x-\frac{4p}{x}$$

Solve for p

$$p=\frac{x\left(2x-k\right)}{4}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2x^{2}-kx=4p$$

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

$$4p=2x^{2}-kx$$

Divide both sides by 4.

$$\frac{4p}{4}=\frac{x\left(2x-k\right)}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$p=\frac{x\left(2x-k\right)}{4}$$