by multiplying both sides of the equation by x^1/2 and using a suitable substitution solve:
2x^1/2=12x^(-1/2)-5
+128474 2x^(1/2) = 12 / x^(1/2) - 5 multiplying through by x^(1/2) we get
2x = 12 - 5x^(1/2)
2x - 12 = - 5x^(1/2) square both sides
4x^2 - 48x + 144 = 25x
4x^2 - 73x + 144 = 0 factor as
(4 x - 9) ( x - 16) = 0
Setting both factors to 0 and solving for x we get that
x = 9/4 or x =16
Which is true ????
If x = 9/4 then x^(1/2) = 3/2
2 (3/2) = 12 / (3/2) - 5
3 = 8 - 5 true
If x = 16 then x^(1/2) = 4
2(4) = 12 / 4 - 5
8 = 3 - 5 not true
The answer is x = 9/4
We get the extraneous answer of x =16 because of squaring......this often happens !!!!
