What is 3+4*5/2*3-7²+6/3? 

Firstly we do the powers, then multiplications and divisions, then additions and substractions. So:

3 + 4 * 5 / 2 * 3 - 7² + 6 / 3 =
= 3 + 4 * 5 / 2 * 3 + 49 + 6 / 3 =
= 3 + 20 / 2 * 3 + 49 + 6 / 3 =
= 3 + 10 * 3 + 49 + 6 / 3 =
= 3 + 30 + 49 + 2 =
= 33 + 51 =
= 84