Solve sqrt{d}+y/sqrt{d}=8

$$\sqrt { d } + \frac { y } { \sqrt { d } } = 8$$

Solve for y (complex solution)

$$y=-d+8\sqrt{d}$$

$$d\neq 0$$

Steps for Solving Linear Equation

Subtract \sqrt{d} from both sides.

$$\frac{y}{\sqrt{d}}=8-\sqrt{d}$$

The equation is in standard form.

$$\frac{1}{\sqrt{d}}y=-\sqrt{d}+8$$

Divide both sides by \left(\sqrt{d}\right)^{-1}.

$$\frac{\frac{1}{\sqrt{d}}y\sqrt{d}}{1}=\frac{\left(-\sqrt{d}+8\right)\sqrt{d}}{1}$$

Dividing by \left(\sqrt{d}\right)^{-1} undoes the multiplication by \left(\sqrt{d}\right)^{-1}.

$$y=\frac{\left(-\sqrt{d}+8\right)\sqrt{d}}{1}$$

Divide 8-\sqrt{d} by \left(\sqrt{d}\right)^{-1}.

$$y=-d+8\sqrt{d}$$

Solve for y

$$y=-d+8\sqrt{d}$$

$$d>0$$

Steps for Solving Linear Equation

Subtract \sqrt{d} from both sides.

$$\frac{y}{\sqrt{d}}=8-\sqrt{d}$$

The equation is in standard form.

$$\frac{1}{\sqrt{d}}y=-\sqrt{d}+8$$

Divide both sides by \left(\sqrt{d}\right)^{-1}.

$$\frac{\frac{1}{\sqrt{d}}y\sqrt{d}}{1}=\frac{\left(-\sqrt{d}+8\right)\sqrt{d}}{1}$$

Dividing by \left(\sqrt{d}\right)^{-1} undoes the multiplication by \left(\sqrt{d}\right)^{-1}.

$$y=\frac{\left(-\sqrt{d}+8\right)\sqrt{d}}{1}$$

Divide 8-\sqrt{d} by \left(\sqrt{d}\right)^{-1}.

$$y=-d+8\sqrt{d}$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=-y-8\sqrt{16-y}+32\text{, }&y\neq 0\text{ and }arg(-\sqrt{16-y}+4)<\pi \\d=\left(\sqrt{16-y}+4\right)^{2}\text{, }&arg(\sqrt{16-y}+4)<\pi \end{matrix}\right.$$

Solve for d

$$\left\{\begin{matrix}d=-y-8\sqrt{16-y}+32\text{, }&y\neq 0\text{ and }y\leq 16\text{ and }-\sqrt{16-y}+4\geq 0\\d=\left(\sqrt{16-y}+4\right)^{2}\text{, }&y\leq 16\end{matrix}\right.$$