The phrase 'essentially solved' is correct and usable in written English.
You can use it when you want to indicate that a problem or issue has been mostly or largely solved but not completely resolved. For example: "The dispute between the two countries has been essentially solved, but there are still a few outstanding issues to be addressed."
The revisions have essentially solved whatever design problems arose under the prior regulations.
By turning physical property into endlessly duplicable e-property, the ancient human problem of "mine-thine" has been essentially solved.
I was somewhat skeptical when Senator Bernie Sanders, an independent from Vermont, told me that these centers (there are 39 sites of various size in the state) had "essentially solved the problem of primary care" for local residents.
By using a flexible, market-based approach, we have essentially solved the problem of acid rain — meeting the program's targets three years ahead of schedule and at a fraction of the expected costs.
As recounted by Sakharov, this test "crowned years of effort [and] opened the way for a whole range of devices with remarkable capabilities…it had essentially solved the problem of creating high-performance thermonuclear weapons".
Through the agency's Materials Analysis Unit, about half of whose work is in geology, I had arranged to interview Special Agent Ronald Rawalt, a mineralogist and paleontologist who had performed a feat of geological espionage in Mexico that had essentially solved the murder of an American drug agent there.
Do you think that weakening the ties between those industries would essentially solve the problem of overuse of medication?
And it would essentially solve our medium-term deficit problem, reducing the deficit by $200 billion to $350 billion a year from 2015 to 2020.
In "Darwin's Black Box," Behe speculated that the designer might have assembled the first cell, essentially solving the problem of irreducible complexity, after which evolution might well have proceeded by more or less conventional means.
Martin Fleischmann made the greatest discovery since fire: replicating the furnace of the sun at room temperature in a jar of water, essentially solving the world's energy needs forever.
Hutter (2005, 2007a,b) argues that Solomonoff's formal and complete theory essentially solves the induction problem.
