19. \( (2 x-5)^{\frac{1}{2}}-7=0 \)

To solve the equation \( (2x - 5)^{\frac{1}{2}} - 7 = 0 \), first isolate the square root term. Add 7 to both sides to get \( (2x - 5)^{\frac{1}{2}} = 7 \). Next, square both sides to eliminate the square root, resulting in \( 2x - 5 = 49 \). Now, add 5 to both sides to obtain \( 2x = 54 \), and then divide by 2 to find \( x = 27 \). To verify, substitute \( x = 27 \) back into the original equation: \( (2(27) - 5)^{\frac{1}{2}} - 7 = (54 - 5)^{\frac{1}{2}} - 7 = (49)^{\frac{1}{2}} - 7 = 7 - 7 = 0 \). Thus, the solution is confirmed to be \( x = 27 \).