find the consecutives integers such that 3 times the square of yhe first is equal to 7 more than 5 times the second.

Consecutive integers can be represented as:

x, x+1, x+2,.

3 times the square of the first:

3\cdot x^{2}

7 more than 5 times the second:

5(x+1)+7

Set these equal and solve for x.