Help me solve this. Please show me the work so I know how to do it.

The difference between a number and twice it's reciprocal is 17/10.

x - 2(1/x) = 17/10

multiply each term by 10x

10x^2 - 20 = 17x
10x^2 - 17x - 20 = 0
(5x + 4)(2x - 5) = 0

so x = -4/5 or x = 5/2

check:
reciprocal of 5/2 is 2/5
twice the reciprocal is 4/5
evaluate 5/2 - 4/5
= (25-8)/10 = 17/10

I will let you check the other the same way