Solve sqrt{2w-t/3}=6

$$\sqrt { \frac { 2 w - t } { 3 } } = 6$$

Solve for t

$$t=2\left(w-54\right)$$

Steps for Solving Radical Equations

Divide each term of 2w-t by 3 to get \frac{2}{3}w-\frac{1}{3}t.

$$\sqrt{\frac{2}{3}w-\frac{1}{3}t}=6$$

Square both sides of the equation.

$$-\frac{1}{3}t+\frac{2w}{3}=36$$

Subtract \frac{2}{3}w from both sides of the equation.

$$-\frac{1}{3}t+\frac{2w}{3}-\frac{2w}{3}=36-\frac{2w}{3}$$

Subtracting \frac{2}{3}w from itself leaves 0.

$$-\frac{1}{3}t=36-\frac{2w}{3}$$

Subtract \frac{2}{3}w from 36.

$$-\frac{1}{3}t=-\frac{2w}{3}+36$$

Multiply both sides by -3.

$$\frac{-\frac{1}{3}t}{-\frac{1}{3}}=\frac{-\frac{2w}{3}+36}{-\frac{1}{3}}$$

Dividing by -\frac{1}{3} undoes the multiplication by -\frac{1}{3}.

$$t=\frac{-\frac{2w}{3}+36}{-\frac{1}{3}}$$

Divide 36-\frac{2w}{3} by -\frac{1}{3} by multiplying 36-\frac{2w}{3} by the reciprocal of -\frac{1}{3}.

$$t=2w-108$$

Solve for w

$$w=\frac{t+108}{2}$$

Steps for Solving Radical Equations

Divide each term of 2w-t by 3 to get \frac{2}{3}w-\frac{1}{3}t.

$$\sqrt{\frac{2}{3}w-\frac{1}{3}t}=6$$

Square both sides of the equation.

$$\frac{2}{3}w-\frac{t}{3}=36$$

Subtract -\frac{1}{3}t from both sides of the equation.

$$\frac{2}{3}w-\frac{t}{3}-\left(-\frac{t}{3}\right)=36-\left(-\frac{t}{3}\right)$$

Subtracting -\frac{1}{3}t from itself leaves 0.

$$\frac{2}{3}w=36-\left(-\frac{t}{3}\right)$$

Subtract -\frac{1}{3}t from 36.

$$\frac{2}{3}w=\frac{t}{3}+36$$

Divide both sides of the equation by \frac{2}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{2}{3}w}{\frac{2}{3}}=\frac{\frac{t}{3}+36}{\frac{2}{3}}$$

Dividing by \frac{2}{3} undoes the multiplication by \frac{2}{3}.

$$w=\frac{\frac{t}{3}+36}{\frac{2}{3}}$$

Divide 36+\frac{t}{3} by \frac{2}{3} by multiplying 36+\frac{t}{3} by the reciprocal of \frac{2}{3}.

$$w=\frac{t}{2}+54$$