Three charges, Q1, Q2 and Q3 are located on a straight line. The charge Q3 is located 0.169 m to the right of Q2. The charges Q1 = 1.56 μC and Q2 = -3.03 μC are fixed at their positions, distance 0.268 m apart, and the charge Q3 = 3.18 μC could be moved along the line. For what position of Q3 relative to Q1 is the net force on Q3 due to Q1 and Q2 zero? Give your answer in meters, and use the plus sign for Q3 to the right of Q1.
Coulomb's Law: F=(k(q^2))/r^2
The Attempt at a Solution
(k*Q3*Q2)/r^2 = (k*Q3*Q1)/ (r+0.268)^2
After setting it up, I noticed that k and Q3 on both sides cancel out which leaves me with:
(Q2)/r^2 = (Q1)/ (r+0.268)^2
(3.02*10^-6)/r^2 = (1.56*10^-6)/(r+0.268)^2
Then, I got a quadratic formula: 1.47*r^2 + 1.62*r +.2176
so r is equal to -0.157m and -0.945m
but none of the two is right. What am I doing wrong?