Solve 6sqrt{2m-n}=5t

$$6 \sqrt { 2 m - n } = 5 t$$

Solve for m

$$m=\frac{25t^{2}}{72}+\frac{n}{2}$$

$$t\geq 0$$

Steps for Solving Radical Equations

Divide both sides by 6.

$$\frac{6\sqrt{2m-n}}{6}=\frac{5t}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$\sqrt{2m-n}=\frac{5t}{6}$$

Square both sides of the equation.

$$2m-n=\frac{25t^{2}}{36}$$

Subtract -n from both sides of the equation.

$$2m-n-\left(-n\right)=\frac{25t^{2}}{36}-\left(-n\right)$$

Subtracting -n from itself leaves 0.

$$2m=\frac{25t^{2}}{36}-\left(-n\right)$$

Subtract -n from \frac{25t^{2}}{36}.

$$2m=\frac{25t^{2}}{36}+n$$

Divide both sides by 2.

$$\frac{2m}{2}=\frac{\frac{25t^{2}}{36}+n}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$m=\frac{\frac{25t^{2}}{36}+n}{2}$$

Divide \frac{25t^{2}}{36}+n by 2.

$$m=\frac{25t^{2}}{72}+\frac{n}{2}$$

Solve for n

$$n=-\frac{25t^{2}}{36}+2m$$

$$t\geq 0$$

Steps for Solving Radical Equations

Divide both sides by 6.

$$\frac{6\sqrt{-n+2m}}{6}=\frac{5t}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$\sqrt{-n+2m}=\frac{5t}{6}$$

Square both sides of the equation.

$$-n+2m=\frac{25t^{2}}{36}$$

Subtract 2m from both sides of the equation.

$$-n+2m-2m=\frac{25t^{2}}{36}-2m$$

Subtracting 2m from itself leaves 0.

$$-n=\frac{25t^{2}}{36}-2m$$

Divide both sides by -1.

$$\frac{-n}{-1}=\frac{\frac{25t^{2}}{36}-2m}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$n=\frac{\frac{25t^{2}}{36}-2m}{-1}$$

Divide \frac{25t^{2}}{36}-2m by -1.

$$n=-\frac{25t^{2}}{36}+2m$$

Solve for m (complex solution)

$$m=\frac{25t^{2}}{72}+\frac{n}{2}$$

$$arg(t)<\pi \text{ or }t=0$$

Solve for n (complex solution)

$$n=-\frac{25t^{2}}{36}+2m$$

$$arg(t)<\pi \text{ or }t=0$$