A natural number, when increased by 12, equals . . .

Question : A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.

Doubt by Jayant

Solution :  

Let the natural number be x
ATQ

x+12=160(1/x)
(x+12)x=160
x²+12x=160
x²+12x-160=0
x²+(20-8)x-160=0
x²+20x-8x-160=0
x(x+20)-8(x+20)=0
(x-8)(x+20)=0

x+20=0
x=-20

But x is a natural number 
so x≠-20

x-8=0
x=8

Hence, the required natural number is 8.