Solve sqrt{2m}-2ym=1

$$\sqrt { 2 m } - 2 y m = 1$$

Solve for y

$$y=\frac{\sqrt{2m}-1}{2m}$$

$$m>0$$

Steps for Solving Linear Equation

Subtract \sqrt{2m} from both sides.

$$-2ym=1-\sqrt{2m}$$

The equation is in standard form.

$$\left(-2m\right)y=-\sqrt{2m}+1$$

Divide both sides by -2m.

$$\frac{\left(-2m\right)y}{-2m}=\frac{-\sqrt{2m}+1}{-2m}$$

Dividing by -2m undoes the multiplication by -2m.

$$y=\frac{-\sqrt{2m}+1}{-2m}$$

Divide 1-\sqrt{2m} by -2m.

$$y=\frac{1}{\sqrt{2m}}-\frac{1}{2m}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{2y-\sqrt{1-4y}-1}{4y^{2}}\text{, }&y>0\text{ and }y\leq \frac{1}{4}\\m=-\frac{2y+\sqrt{1-4y}-1}{4y^{2}}\text{, }&y\leq \frac{1}{4}\text{ and }y\neq 0\\m=\frac{1}{2}=0.5\text{, }&y=0\end{matrix}\right.$$