Solve x-15y-2sqrt{2x}y=0

$$x-15y-2 \sqrt{ 2x } y = 0$$

Solve for y (complex solution)

$$y=\frac{x}{2\sqrt{2x}+15}$$

Steps for Solving Linear Equation

Multiply -1 and 2 to get -2.

$$x-15y-2\sqrt{2x}y=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$-15y-2\sqrt{2x}y=-x$$

Combine all terms containing y.

$$\left(-15-2\sqrt{2x}\right)y=-x$$

The equation is in standard form.

$$\left(-2\sqrt{2x}-15\right)y=-x$$

Divide both sides by -15-2\sqrt{2x}.

$$\frac{\left(-2\sqrt{2x}-15\right)y}{-2\sqrt{2x}-15}=-\frac{x}{-2\sqrt{2x}-15}$$

Dividing by -15-2\sqrt{2x} undoes the multiplication by -15-2\sqrt{2x}.

$$y=-\frac{x}{-2\sqrt{2x}-15}$$

Divide -x by -15-2\sqrt{2x}.

$$y=\frac{x}{2\sqrt{2x}+15}$$

Solve for y

$$y=\frac{x}{2\sqrt{2x}+15}$$

$$x\geq 0$$

Steps for Solving Linear Equation

Multiply -1 and 2 to get -2.

$$x-15y-2\sqrt{2x}y=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$-15y-2\sqrt{2x}y=-x$$

Combine all terms containing y.

$$\left(-15-2\sqrt{2x}\right)y=-x$$

The equation is in standard form.

$$\left(-2\sqrt{2x}-15\right)y=-x$$

Divide both sides by -15-2\sqrt{2x}.

$$\frac{\left(-2\sqrt{2x}-15\right)y}{-2\sqrt{2x}-15}=-\frac{x}{-2\sqrt{2x}-15}$$

Dividing by -15-2\sqrt{2x} undoes the multiplication by -15-2\sqrt{2x}.

$$y=-\frac{x}{-2\sqrt{2x}-15}$$

Divide -x by -15-2\sqrt{2x}.

$$y=\frac{x}{2\sqrt{2x}+15}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=y\left(2\sqrt{\frac{2\left(2y+15\right)}{y}}y+4y+15\right)\text{, }&arg(\left(2\sqrt{1+\frac{15}{2y}}+2\right)y)<\pi \text{ and }y\neq 0\\x=y\left(-2\sqrt{\frac{2\left(2y+15\right)}{y}}y+4y+15\right)\text{, }&arg(\left(-2\sqrt{1+\frac{15}{2y}}+2\right)y)<\pi \text{ and }y\neq 0\\x=0\text{, }&\sqrt{2}y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=y\left(2\sqrt{2y\left(2y+15\right)}+4y+15\right)\text{, }&\sqrt{16+\frac{120}{y}}y^{2}+4y^{2}+15y\geq 0\text{ and }y>0\\x=0\text{, }&\sqrt{2}y=0\end{matrix}\right.$$