Solve congruence: $45x \equiv 15 \pmod{78}$ (What am I doing wrong?)
Solution 1:
When you divide through by 3, the resulting congruence should be $$15x\equiv 5\pmod{26},$$ not $$15x\equiv 3\pmod{26}.$$
Solution 2:
Everything you did is perfectly correct, except one small thing:
$$15/3=5.$$