Bonsoir,
1) [tex]F_T=6,6742\times10^{-17}\times\dfrac{5,9736\times10^{24}\times m}{x^2}\\\\F_T=\dfrac{398690011,2\times m}{x^2}\ Newtons\\\\F_L=6,6742\times10^{-17}\times\dfrac{7,349\times10^{22}\times m}{x^2}\\\\F_L=\dfrac{4904869,58\times m}{(384000-x)^2}\ Newtons[/tex]
2) [tex]\dfrac{G\times m_T\times m}{x^2}=\dfrac{G\times m_L\times m}{(384000-x)^2}\\\\\\\Longleftrightarrow\dfrac{m_T}{x^2}=\dfrac{m_L}{(384000-x)^2}\\\\\Longleftrightarrow\dfrac{(384000-x)^2}{x^2}=\dfrac{m_L}{m_T}\\\\\\\Longleftrightarrow(\dfrac{384000-x}x)^2=\dfrac{m_L}{m_T}\\\\\\\Longleftrightarrow\dfrac{384000-x}x=\sqrt{\dfrac{m_L}{m_T}}[/tex]
[tex]\Longleftrightarrow\dfrac{384000-x}x=\sqrt{\dfrac{7,349\times10^{22}}{5,9736\times10^{24}}}\\\\\Longleftrightarrow\dfrac{384000-x}x\approx0,1109164739\\\\\Longleftrightarrow384000-x\approx0,1109164739\times x\\\\\Longleftrightarrow384000\approx0,1109164739\times x+x\\\\\Longleftrightarrow384000\approx1,1109164739\times x\\\\\Longleftrightarrow x\approx\dfrac{384000}{1,1109164739}\\\\\Longleftrightarrow x\approx 345660\ km[/tex]