Solve for a (45-2a)^(1/2)=(a-6)^(1/2)

${(45 - 2 a)}^{\frac{1}{2}} = {(a - 6)}^{\frac{1}{2}}$

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$45 - 2 a = a - 6$

Solve for $a$ .

Move all terms containing $a$ to the left side of the equation.

Subtract $a$ from both sides of the equation.

$45 - 2 a - a = - 6$

Subtract $a$ from $- 2 a$ .

$45 - 3 a = - 6$

Move all terms not containing $a$ to the right side of the equation.

Subtract $45$ from both sides of the equation.

$- 3 a = - 6 - 45$

Subtract $45$ from $- 6$ .

$- 3 a = - 51$

Divide each term in $- 3 a = - 51$ by $- 3$ and simplify.

Divide each term in $- 3 a = - 51$ by $- 3$ .

$\frac{- 3 a}{- 3} = \frac{- 51}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 a}{- 3} = \frac{- 51}{- 3}$

Divide $a$ by $1$ .

$a = \frac{- 51}{- 3}$

Simplify the right side.

Divide $- 51$ by $- 3$ .

$a = 17$