Question 931674
Let x   = the original number
    1/x = the reciprocal number


The positive number which diminished by 14 is equal to 51 times the reciprocal of the number.
x-14=51(1/x)
x-14=51/x
x(x-14)=51
x^2-14x=51
x^2-14x-51=0
(x-17)(x+3)=0
x=17
or
x=-3

The number is 17.

Check
17-14=51(1/17)
    3=51/17
    3=3