For example, 7x² - x³ ≤ -x² + 5x + 6 tells me that one of the solutions is 1.40555 even though it's not. The number I really needed is 1.405545.
When I put this into Wolfram Alpha, I can see "More digits" in the "Solution" section. If I click "More digits", I see something like
-0.59385395717500431267<=x<=1.4055454265503667681
Is that what you want?
I don't know how I didn't see that, thank you!