I don't think your c value is correct (because if you use the values you provided in the question, there are no real solutions). I believe the c value should actually be -0.0029. If so, then you would plug a=4, b=0.0059 and c=-0.0029 in the quadratic equation: (-b+/-sqrt(b^2-4*a*c))/(2*a)

This would result in solutions of -0.028 and 0.026 just as your teacher has calculated.