Let the two consecutive numbers be x and x+1

Reciprocals are 1/x and

1/(x+1)

Sum of numbers is given as -9/20

Which can be written as

1/x + 1/(x+1) = -9/20

(x+1+x)/x(x+1)=-9/20

2x+1/x^2+x=-9/20

20(2x+1)=-9(x^2+x)

40x+20=9x^2+9x

9x^2-31x-20=0

9x^2-36x+5x-20=0

(9x+5)(x-4)=0

X=-5/9 and x=4

The number cannot be negative so we will consider only x=4

X+1=5