Where on the X-Axis is the Net Electric Force Zero?

[Zackkkkkk]

1.An electric charge q1 (-e) is located at the origin. A second electric charge q2 (-4e) is located at a distance d from the origin on the x-axis. A third charge q3 (+e) is located a distance x, which is less than d, on the x-axis between q1 and q2. In terms of d, what is the distance x where the net electric force is zero?

2. I just need a pretty thorough explanation. Not a broken stream of steps.F = F1 - F2
F = 0
then
F1 = F2
kq1q3 / x^2 = kq2q3 / (d-x)^2
q1 / x^2 = q2 / (d-x)^2
(d-x)^2 - (q2/q1)x^2 = 0
...

I've made it as far as this and then asked for help on another site. Someone responded with the following:

F = F1 - F2 [forces are opposite]
F = 0
then
F1 = F2
kq1q3 / x^2 = kq2q3 / (d-x)^2
q1 / x^2 = q2 / (d-x)^2
(d-x)^2 - (q2/q1)x^2 = 0
(1-q2/q1)x^2 -2dx + d^2 = 0
-3x^2 -2dx + d^2 = 0
x = [2d +- (4d^2 - 12d^2)^1/2] / (-6)
x = d/3

I have no clue what he/she did after line 9 (-3x^2 -2dx+d^2 = 0).

 

[haruspex]

-3x^2 -2dx + d^2 = 0
x = [2d +- (4d^2 - 12d^2)^1/2] / (-6)
x = d/3

I have no clue what he/she did after line 9 (-3x^2 -2dx+d^2 = 0).

She just applied the standard formula for solving a quadratic.

 

[Zackkkkkk]

She just applied the standard formula for solving a quadratic.

I figured it out. Thanks.