net gravitational force?

Question

Question: Find the point between Saturn and the Sun at which an object can be placed so that the net gravitational force exerted by Saturn and Sun on this object is zero.

mass of sun: 1.991 x 10^30
mass of saturn: 5.68 x 10^26
distance between sun and saturn: 1.43 x 10^12

i set the forces equal to each other
GmMsun/r^2 = GmMsaturn/ (d-r)^2

where d is the distance between the two.

I cancelled out common terms and got
Msun/r^2 = Msaturn/ (d-r)^2

I plugged in the values and then tried to solve for r using the quadratic equation, butI kept getting a nonreal answer. any help would be appreciated!

Answer 1

F1-F2=0

GM1m/R^2 - GM2m/(D-R)^2=0
M1- mass of Saturn
M2 - mass of the Sun
D- distance between Sun and Saturn
R - distance from Saturn to the object

M1/R^2= M2/(D-R)^2
or
M2R^2=M1D^2 - 2M1DR + M1R^2
(M1-M2)R^2 - 2M1DR + M1D^2 =0
Just solve for R quadratic equation
aR^2 -bR + c=0

Answer 2

You're doing the right thing, but probably plugging in numbers too early and making sign errors. Continue simplifying the symbolic expression until you have a quadratic equation for r. Then plug in numbers. Less chance of a sign error that way.