Find the x and y coordinates of the position at which an electron would be in equilibrium.

Let e be the charge of the electron.
Then F1 + F2 = 0
F1 = K (-1.5) * (-e) /r1^2
F2 = K (15) * (-e) /r2^2
(-1.5) * /r1^2 + (15) /r2^2 = 0
-1 /r1^2 + (10) /r2^2 = 0
[r2/r1]^2 = 10
[R2/r1] = ± 3.162
r2 = ± 3.162 r1.

Given r1 + r2 = √ [1^2 + 0.5^2] = 1.11801
Also tan θ = 0.5 => θ = 26.57°

Substituting r2 = 3.162 r1 in 1
4.162 r1=1.1180
r1 = 0.2686 m

x coordinate = r1 cos θ = 0.2403 m
y coordinate = r1 sin θ = 0.1201m


Substituting r2 = - 3.162 r1 in 1
-2.162 r1=1.1180
r1 = -0.5171m
x coordinate = r1 cos θ = -0.4625m
y coordinate = r1 sin θ = -0.2313m

Look it up you feel me