Point charge problem?

Question

Sum of two point charges is +6 uC. when they are 2 cm apart each experiences a force of 200 N. find the charges given that both charges are positive

please show work, person that shows work and correct answer gets best answer

Answer 1

F = kq1q2/r^2 = 9E9*q1*(6e-6-q1)/0.02^2 = 200 N

This results in a quadratic:

-q1^2 + 6e-6q1 = 200*0.02^2/9E9

-q1^2 + 6e-6q1 - 200*0.02^2/9E9 = 0

The roots are:

q1 = 2.6667E-6 C (and q2 = 3.3333E-6 C)

and

q1 = 3.3333E-6 C (and q2 = 2.6667E-6 C)