Solve x+frac{sqrt{y}}{9}=1/5

$$x + \frac { \sqrt { y } } { 9 } = 1 / 5$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{y}}{9}+\frac{1}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 45, the least common multiple of 9,5.

$$45x+5\sqrt{y}=9$$

Subtract 5\sqrt{y} from both sides.

$$45x=9-5\sqrt{y}$$

The equation is in standard form.

$$45x=-5\sqrt{y}+9$$

Divide both sides by 45.

$$\frac{45x}{45}=\frac{-5\sqrt{y}+9}{45}$$

Dividing by 45 undoes the multiplication by 45.

$$x=\frac{-5\sqrt{y}+9}{45}$$

Divide 9-5\sqrt{y} by 45.

$$x=-\frac{\sqrt{y}}{9}+\frac{1}{5}$$

Solve for x

$$x=-\frac{\sqrt{y}}{9}+\frac{1}{5}$$

$$y\geq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 45, the least common multiple of 9,5.

$$45x+5\sqrt{y}=9$$

Subtract 5\sqrt{y} from both sides.

$$45x=9-5\sqrt{y}$$

The equation is in standard form.

$$45x=-5\sqrt{y}+9$$

Divide both sides by 45.

$$\frac{45x}{45}=\frac{-5\sqrt{y}+9}{45}$$

Dividing by 45 undoes the multiplication by 45.

$$x=\frac{-5\sqrt{y}+9}{45}$$

Divide 9-5\sqrt{y} by 45.

$$x=-\frac{\sqrt{y}}{9}+\frac{1}{5}$$

Solve for y

$$y=\frac{81\left(1-5x\right)^{2}}{25}$$

$$\frac{9}{5}-9x\geq 0$$

Steps for Solving Radical Equations

Subtract x from both sides of the equation.

$$\frac{1}{9}\sqrt{y}+x-x=\frac{1}{5}-x$$

Subtracting x from itself leaves 0.

$$\frac{1}{9}\sqrt{y}=\frac{1}{5}-x$$

Multiply both sides by 9.

$$\frac{\frac{1}{9}\sqrt{y}}{\frac{1}{9}}=\frac{\frac{1}{5}-x}{\frac{1}{9}}$$

Dividing by \frac{1}{9} undoes the multiplication by \frac{1}{9}.

$$\sqrt{y}=\frac{\frac{1}{5}-x}{\frac{1}{9}}$$

Divide \frac{1}{5}-x by \frac{1}{9} by multiplying \frac{1}{5}-x by the reciprocal of \frac{1}{9}.

$$\sqrt{y}=\frac{9}{5}-9x$$

Square both sides of the equation.

$$y=\frac{81\left(1-5x\right)^{2}}{25}$$

Solve for y (complex solution)

$$y=\frac{81\left(1-5x\right)^{2}}{25}$$

$$x=\frac{1}{5}\text{ or }arg(\frac{9}{5}-9x)<\pi$$