Over a period of more than 30 years, albert klein of california drove 2.5 × 106 km in one automobile. consider two charges, q1 = 2.0 c and q2 = 6.0 c, separated by klein's total driving distance. a third charge, q3 = 4.0 c, is placed on the line connect- ing q1 and q2. how far from q1 should q3 be placed for q3 to be in equilibrium

For q3 to be in equilibrium the total force acting on it has to be zero.
Let's say that total distance traveled by car is L (this is just for the convenience).
We can set up a system of equations to find an answer. Let's say that from q1 to q3 the distance is r_1 and from q3 to q2 the distance is r_2, we know that this distance has to be equal to:

The second equation is going to the total force acting on the charge q3:

k_c is the Coulomb's constant. Since left-hand side is zero we just divide whole equation with k_c to get rid of it:

Let's solve this for r_1^2:

Now we have a quadratic equation with following parameter:

We know that two solutions are:

We need a positive solution. When we plug in all the numbers we get: