I can\'t get the algebra of the second part right. Please help! A 115-kg object

Question

I can't get the algebra of the second part right. Please help!

A 115-kg object and a 415-kg object are separated by 4.50 m. Find the magnitude of the net gravitational force exerted by these objects on a 57.0-kg object placed midway between them. At what position (other than an infinitely remote one) can the 57.0-kg object be placed so as to experience a net force of zero from the other two objects? Draw a careful picture and label the distance between the 415 kg object and the 57.0 kg object as x. m from the 415 kg mass toward the 115 kg mass

Explanation / Answer

it can be only in middle of them at any where because gravitational force always attracts so

suppose it is x m from 115 kg so

F1 = F2

G*115*57 / x^2 = G*415*57/( 4.5-x)^2

115/x^2 = 415/(4.5-x)^2 solve this for x nd we got

x= -5 ( this is not possible ) & 1.552 ( this is possible)

so

x = 1.552 m from 115 Kg

or ( 4.5-1.552) m = 2.95 kg from 415 kg

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