$\sqrt{3-x}-\sqrt{-x^2+8x+10}=1$ Consider the equation
$$
\sqrt{3-x}-\sqrt{-x^2+8x+10}=1.
$$
I have solved it in a dumb way by solving the equation of degree four. So, the
only real solution is $x = -1$. Can you please suggest, maybe there are better or easier ways to solve it?

You did it in the right way. You will end up with a $x^4$ term, and you must solve from there to get $-1.$
The above answer is right, that it gives you a $range$ of values, but if you want to solve directly, you must do it the way you have said above.
