at what coordinate on the axis is the net electric field of the particles zero?

Question

8 In Figure 22-30, particle 1 of charge q1 = –5.00q and particle 2 of charge q2 = +2.00q are fixed to an x axis. (a) As a multiple of distance L, at what coordinate on the axis is the net electric field of the particles zero? (b) Sketch the net electric field lines.
Fig. 22-30 Problem 8.
http://lowellphysics.org/beta/resources/CH22/Problems/c22x22_11.xform.html

Answer 1

Assume that the net electric field of the particles is zero at location kL on the axis.
The E-field due to q1 is:
-5q/(4*pi*epsilon_0*k^2*L^2)
The E-field due to q2 is:
2q/(4*pi*epsilon_0*(k-1)^2*L^2)
(a) According to the problem,
-5q/(4*pi*epsilon_0*k^2*L^2) + 2q/(4*pi*epsilon_0*(k-1)^2*L^2) = 0
or: -5/k^2 + 2/(k-1)^2 = 0
-5(k-1)^2 + 2*k^2 = 0
3*k^2 - 10k + 5 = 0
k = (5 +- sqrt(10))/3
(b) Try it yourself.

Answer 2

I feel some small but vital info is being left out as relates to L.
Is there a sketch or diagram there relating L to the x axis?
On X axis means y=0, for all values. So two points (2q,0) and (-5q,0) . adding these two together as vectors we have (-3q,0)
as the resultant. to nullify that vector we would have (3q,0). The L part is making no sense to me. 3/7L ?