1/7 (x+9)^3/2=49
(1/7) (x+9)^(3/2)=49 multiply both sides by 7
(x + 9)^(3/2) = 343 raise each side to the 2/3 power
x + 9 = (343)^(2/3) = [ (343^(1/3)] ^2 = 7^2 = 49
So
x + 9 = 49 subtract 9 from both sides
x = 40 [as the only real solution]