Solve 3m-1/4=frac{sqrt{2n}}{2}

$$\frac { 3 m - 1 } { 4 } = \frac { \sqrt { 2 n } } { 2 }$$

Solve for m

$$m=\frac{2\sqrt{2n}+1}{3}$$

$$n\geq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$3m-1=2\sqrt{2n}$$

Add 1 to both sides.

$$3m=2\sqrt{2n}+1$$

Divide both sides by 3.

$$\frac{3m}{3}=\frac{2\sqrt{2n}+1}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$m=\frac{2\sqrt{2n}+1}{3}$$

Solve for n

$$n=\frac{\left(3m-1\right)^{2}}{8}$$

$$m\geq \frac{1}{3}$$

Steps for Solving Radical Equations

Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$3m-1=2\sqrt{2n}$$

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

$$2\sqrt{2n}=3m-1$$

Divide both sides by 2.

$$\frac{2\sqrt{2n}}{2}=\frac{3m-1}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\sqrt{2n}=\frac{3m-1}{2}$$

Square both sides of the equation.

$$2n=\frac{\left(3m-1\right)^{2}}{4}$$

Divide both sides by 2.

$$\frac{2n}{2}=\frac{\left(3m-1\right)^{2}}{2\times 4}$$

Dividing by 2 undoes the multiplication by 2.

$$n=\frac{\left(3m-1\right)^{2}}{2\times 4}$$

Divide \frac{\left(-1+3m\right)^{2}}{4} by 2.

$$n=\frac{\left(3m-1\right)^{2}}{8}$$