Assume toward a contradiction that
x
is an integer satisfying
18
x
2
+ 39
x
– 7 = 0.
Then reducing the equation modulo 3 gives
0
x
2
+ 0
x
+ 2 ≡ 0 mod 3,
In other words, 2 ≡ 0 mod 3, which is a contradiction.
