Your question is reopened now. Since I am the one who both voted to close and reopen your question, I may briefly explain my action (though I think the generic comment in the 'off topic' vote is clear enough in this case).
As noted by Gerry in the comment, my vote was cast when the question is still in the first edit. This question should be closed as you did not give any hint what do you know about the question. Do you, for example, know intermediate value theorem? Are you aware that the function is continuous on $(1,2)$? Or, instead you were trying to algebraically solve the equation?
Without knowing the method you used, there is no hint about your background and it is hard to provide an answer for you. Also, in some case some users provide an answer which is not comprehensible by the OP, or it is not what they want, the OP might point that out by commenting in the answer or edit the question. This would be a bad experience for both the answer-er (feel like wasting their time) and other users (which saw an answer not answering the question as requested). (Personally there was an user who kept editing their question after seeing my answer, so I have to make four edits to cope with that!)
To me, the best action is to close the question, so that you can add the essential context and other user are not able to provide (potentially) not helpful answer. Personally, I voted to reopen after seeing the term $[1.1,1.9]$ (around edit 4 I guess), since now it is clear that you are aware of the intermediate value theorem and the singularity at $1$ and $2$. The subsequent comment also make it very clear (to me) where you get stuck.
Closing your question is not really that cruel, IMO. The ultimate goal is to help you get the better answers.