I am a 10th grade student. I appeared in NSTC Screening Test last week and found this problem very difficult. I was unable to solve this. It opens to form a quartic equation. Please upload a video on YouTube for solving equations of this type.

I have plugged this equation in Wolfram Alpha but it requires money, and I don’t own a credit card. If any one has its membership please send me its solution by Wolfram Alpha.

I was able to find the solutions using Wolfram Alpha without issue.

If you intended for the brackets {} to be the fractional part function, please let me know.

Bro, Wolfram's method is not appropriate here. So, I think this equation connected to Pifagor theorem. We have triangle with sides 1 and Sqrt(2)|2-x| and hypothenuse x|2-x|. Also, this equation has this one trigonometric form. In addition, I can say, that given form of equation is a trigonometric equality (with sin(x) and cot(x)). Hope it was useful for you. I tried to solve it whole week. I gave up.

This equation has 21 root and such graph. To solve it, you should solve 21 equations with "a" where a equals integer numbers from 0 to 20)))

Here are not integer solutions and I think that you did a mistake while you wrote it) I did not sleep for 2 weeks due to I wanted to solve it, thank you)