To solve this equation, we first need to simplify the expression on the left side of the equation:

3 3/8 ÷ (1/14x + 5/7) = 27/8 ÷ (1/14x + 5/7)

Next, we can rewrite the division as multiplication by the reciprocal of the second fraction:

27/8 * (7/5) / (1/14x + 5/7)

Now, simplify the expression by multiplying the numerators and denominators separately:

(27 7) / (8 5) / (1/14x + 5/7)
189 / 40 / (1/14x + 5/7)

Now, we can rewrite the fraction division as multiplication by the reciprocal:

189 / 40 * (7/1) / (1/14x + 5/7)

Simplify the expression by multiplying the numerators and denominators:

189 7 / (40 1) / (1/14x + 5/7)
1323 / 40 / (1/14x + 5/7)

The equation now becomes:

1323 / 40 / (1/14x + 5/7) = 2.1

To solve for x, we need to multiply both sides by (1/14x + 5/7):

1323 / 40 = 2.1 * (1/14x + 5/7)

1323 / 40 = 2.1 / 14x + 10.5 / 7

1323 / 40 = 0.15x + 1.5

1323 = 6x + 60

1263 = 6x

x = 210