Two infinite charged lines -- find the locations where E=0

[Grifter]

Homework Statement

A very long (infinite), straight line of charge runs parallel to another very long (infinite) straight line of charge. Both lines are uniformly charged, one with +1*(lambda) and the other with -2*(lambda). The distance between them is d. Find (if any) the location(s) where the electric field is zero.

Homework Equations

[infinite wire] E = 1/(2(pi)(epsilon naught)) * (lambda)/r
[2 wires] E = (sigma1)(sigma2) / 2(epsilon naught)
sigma=area charge
lambda=line charge
epsilon naught=8.854e-12 C^2/N*m^2

The Attempt at a Solution

I drew a picture with the positively charged line with E-lines flowing away and the negatively charged line with E-lines flowing in. Between the E-lines flow from positive to negative. Not sure about the relationship between lambda and sigma or how to use an equation to find E=0 with variable charges.

 

[malawi_glenn]

From a distance r from a wire of charge lenght-density λ (Coloumb per meter) the electric field strenght is proportional to λ/r

You want to solve the equation λ₁/r + λ₂/(d-r) = 0
Just use that λ₂ = -2λ₁ and solve for r in terms of d