Solve Delta=2xr(r+h)

$$\Delta = 2 x r ( r + h )$$

Solve for h (complex solution)

$$\left\{\begin{matrix}h=\frac{\Delta -2xr^{2}}{2rx}\text{, }&r\neq 0\text{ and }x\neq 0\\h\in \mathrm{C}\text{, }&\left(x=0\text{ or }r=0\right)\text{ and }\Delta =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2xr by r+h.

$$\Delta =2xr^{2}+2xrh$$

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

$$2xr^{2}+2xrh=\Delta$$

Subtract 2xr^{2} from both sides.

$$2xrh=\Delta -2xr^{2}$$

The equation is in standard form.

$$2rxh=\Delta -2xr^{2}$$

Divide both sides by 2xr.

$$\frac{2rxh}{2rx}=\frac{\Delta -2xr^{2}}{2rx}$$

Dividing by 2xr undoes the multiplication by 2xr.

$$h=\frac{\Delta -2xr^{2}}{2rx}$$

Divide \Delta -2xr^{2} by 2xr.

$$h=-r+\frac{\Delta }{2rx}$$

Solve for h

$$\left\{\begin{matrix}h=\frac{\Delta -2xr^{2}}{2rx}\text{, }&r\neq 0\text{ and }x\neq 0\\h\in \mathrm{R}\text{, }&\left(x=0\text{ or }r=0\right)\text{ and }\Delta =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2xr by r+h.

$$\Delta =2xr^{2}+2xrh$$

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

$$2xr^{2}+2xrh=\Delta$$

Subtract 2xr^{2} from both sides.

$$2xrh=\Delta -2xr^{2}$$

The equation is in standard form.

$$2rxh=\Delta -2xr^{2}$$

Divide both sides by 2xr.

$$\frac{2rxh}{2rx}=\frac{\Delta -2xr^{2}}{2rx}$$

Dividing by 2xr undoes the multiplication by 2xr.

$$h=\frac{\Delta -2xr^{2}}{2rx}$$

Divide \Delta -2xr^{2} by 2xr.

$$h=-r+\frac{\Delta }{2rx}$$

Solve for r (complex solution)

$$\left\{\begin{matrix}r=\frac{\sqrt{2x\Delta +\left(hx\right)^{2}}}{2x}-\frac{h}{2}\text{; }r=-\frac{\sqrt{2x\Delta +\left(hx\right)^{2}}}{2x}-\frac{h}{2}\text{, }&x\neq 0\\r\in \mathrm{C}\text{, }&\Delta =0\text{ and }x=0\end{matrix}\right.$$

Solve for r

$$\left\{\begin{matrix}r=\frac{\sqrt{2x\Delta +\left(hx\right)^{2}}}{2x}-\frac{h}{2}\text{; }r=-\frac{\sqrt{2x\Delta +\left(hx\right)^{2}}}{2x}-\frac{h}{2}\text{, }&x\neq 0\text{ and }\left(x>0\text{ or }\Delta \leq -\frac{xh^{2}}{2}\right)\text{ and }\left(x<0\text{ or }\Delta \geq -\frac{xh^{2}}{2}\right)\\r\in \mathrm{R}\text{, }&\Delta =0\text{ and }x=0\end{matrix}\right.$$