Given equation of lines are :

      4x + 7y - 3 = 0 .............1

and 2x - 3y + 1 = 0 .............2

Let the required equation of lines having equal intercept is

     x/a + y/a  = 1 

=> x + y = a ..........3

After solving euation 1 and 2, we get

x = 1/13, = 5/13

So (1/3, 5/13) is the point of intersection of the given lines.

Since equation 3 passes through this point, So

     1/13 + 5/13 = a

=> a = 6/13

Now put this value in equation 3, we get

      x + y = 6/13

=> 13(x + y) = 6

=> 13x + 13y = 6 

So equation of line is 13x + 13y = 6