The title of this post is a shorthand, more than an equation: pain greater than fear doesn't so much equal change, as produce change.
It is in the nature of most animals, including humans, to be conservative - not in the ideological/political sense, but in the sense of resisting change. We cling to what we know; we do what we have always done, and especially if someone we consider to be in a position of moral authority has told us to do it.
Conservatism, however, always loses. Whether we speak of biology or society, the species which does not adapt (that means CHANGE) does not survive.
Progress always wins.
Fear of change is finally conquered when the pain of not-changing outweighs the fear.
Non-human animals change their behavior when their environment changes. The brilliant series "Life" points to numerous examples. Sometimes, a mere change of behavior isn't enough: the creatures have to find a new environment. The ones who successfully adapt, survive.
In a society based on representative government, change is typically actuated by the ascendance of a party which promotes greater civil rights. It is never, however, prompted by politicians representing that agenda. What really prompts the change is generally years (or decades) of activism by certain classes of citizens who feel their rights have not advanced at the same rate as those of other citizens.
Expansion of rights comes at no one's expense, but some people always resist it because they view rights as a zero-sum game: you get some, I lose some.
In the U.S., for example, the right to vote has expanded over time; originally, it was only granted to white men who owned property. That class of citizens resisted granting the vote to other classes because as long as they were the only ones who had the right to vote, they could really control everything and keep government favorable to them. So how did the right to vote ever get expanded?
It expanded because eventually the pain of other classes - at NOT having a voice in their own government - outweighed the fear of the propertied white male. Eventually, there were enough of the propertied white men who took the progressive view and understood the pain of the voteless class (also, of course, they may have gotten a little nervous as they began to be seriously outnumbered).
Granting others the right to vote didn't mean propertied white men lost their right to vote: it just meant that their vote no longer was the only controlling vote. Of course, after the first expansion of rights, most propertied white men realized that and adapted. They learned to work with the new classes of voters.
On the family level, an example would be the parents whose child falls in love with someone of a race, religion, or gender other than the parents would have chosen/preferred. Some people have such a strong fear of the Other that they would rather cut the child out of their life than accept change. (And they live out their lives in ever-narrowing enclosures of hostility, anger, and cowardice.)
A majority, however, discover that their love for their child, and the pain of possibly losing that relationship, outweigh the fear. And all of a sudden the unthinkable becomes not such a big deal.
When it comes down to health and fitness, what we see over and over again is the person who knows perfectly well they should manage their weight, their diet, or their vices better. Their pain, however, is not strong enough to overcome their resistance to change.
What typically prompts real change is the first cardiac episode, the diagnosis of Type II diabetes, or another such serious health challenge. All of a sudden the spectre of death is real, and that pain - the pain of realizing life is finite and one's own bad habits can mean losing years of health, not to mention losing years with loved ones - overcomes fear.
So here are some questions to ponder. If we have bad habits that we know we should change, why do we resist? If we find ourselves in negative, critical, blaming thought patterns, why is that? If our first reaction to anything new is resistance, why?
What are we so afraid of?