na złamanie karku po angielsku:

He fell head-long into the river.

as though it had run headlong into a brick wall.

In the headlong rush to buy houses, many people got into debt.

a headlong drive or ride

we move headlong toward our objectives

In the headlong rush to buy houses, many people easily get into debts./ When you break up, the tempation is to rush headlong into a new relationship.