Find all solutions, if any, to each of the following congruencies:

(x^2) -2 is congruent to 0(mod7)

(x^3)-2x+3 is congruent to 0(mod7)

I dont know if I am doing this right this is what I did

gcd(1,-2,7)=1

so there are 1*7 possible solutions

x= 0, 1, 2, 3, 4, 5, 6

solutions of x

-2 not congruent to 0(mod 7)

-1 not congruent to 0(mod 7)

7 congruent to 0(mod 7)

14 congruent to 0(mod 7)

23 not congruent to 0(mod 7)

34 not congruent to 0(mod 7)

so are the solutions 3 and 4 or am i doing it wrong.

I found the second congruency has no solution I hope!!!