4x2-x-5=(4x-5)(x+1)<0, so either 4x-5<0 and x+1>0; or 4x-5>0 and x+1<0.
4x-5<0 and x+1>0: 4x<5, x<5/4 and x>-1 so -1<x<5/4 is a solution, that is, x is between -1 and 5/4 (1¼).
The other condition can't be satisfied because x can't be greater than 1¼ and less than -1 at the same time.