# How to solve irrational inequality [closed]

So task is: $$\sqrt{-x^2+x+6} > 1-x$$... I know the principle of solving tasks with this, but at this task here I have $$\;-x^2+x+6$$ under sqrt and this makes problem for me in forming system and solving it... I did this: https://ibb.co/prrDMrr

## closed as off-topic by Peter, José Carlos Santos, Song, Cesareo, Lee David Chung LinMar 15 at 0:43

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• Please typeset your equations using MathJax. This is unreadable. – Yves Daoust Mar 14 at 21:28
• Welcome to Math.SE! I am having trouble reading the equations that you included in your question. Please format your questions using MathJax. This page should give you a start at learning how to typeset mathematics here so that your posts say what you want them to, and also look good. – Brian Mar 14 at 21:28
• Thanks, I am literally on my phone right now and I don't have access to my computer, so thanks Bernard for editing :) I will read that page and use these functions if I have any questions in future. – Pshyotic Mar 14 at 21:35

The domain of validity of the inequation is defined by the condition $$x^2-x-6\le 0$$ This quadratic polynomial has two integer roots: $$3$$ and $$-2$$, hence the domain of validity is the interval $$[-2,3]$$.
Now, on its domain of validity, $$\sqrt A >B\iff (B<0)\:\text{ or } (A>B^2).$$