number theory - Solve linear congruence for $x$ : $34x ≡ 51( text{mod}; 85)$

Solve the linear congruence for $x$ : $$34x ≡ 51( \text{mod}\; 85)$$

I found using the Euclidean Algorithm that the GCD is $17$. Because the GCD evenly divides $51$, there equivalence should be solvable. I made a Diophantine equation to solve: $34p - 85q = 17$

From using the Euclidean Algorithm I have:

$$85 = 2 \cdot34+17$$

$$34=2 \cdot 17+0$$

$$17=85-2 \cdot34$$

I do not know where to go from here in order to make this model the Diophantine equation in order to solve for $p$, and I'm not entirely sure what to do with the solution when I get it, because I am solving for $x$.