(10/m)-(5/6)=(3/2m)-(5/4)

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Solution for (10/m)-(5/6)=(3/2m)-(5/4) equation: 


D( m )

m = 0

m = 0

m = 0

m in (-oo:0) U (0:+oo)

10/m-(5/6) = (3/2)*m-(5/4) // - (3/2)*m-(5/4)

10/m-((3/2)*m)-(5/6)+5/4 = 0

(-3/2)*m+10/m-5/6+5/4 = 0

10*m^-1-3/2*m^1+5/12*m^0 = 0

(5/12*m^1-3/2*m^2+10*m^0)/(m^1) = 0 // * m^2

m^1*(5/12*m^1-3/2*m^2+10*m^0) = 0

m^1

(-3/2)*m^2+(5/12)*m+10 = 0

(-3/2)*m^2+(5/12)*m+10 = 0

DELTA = (5/12)^2-(4*10*(-3/2))

DELTA = 8665/144

DELTA > 0

m = ((8665/144)^(1/2)-(5/12))/(2*(-3/2)) or m = (-(5/12)-(8665/144)^(1/2))/(2*(-3/2))

m = ((8665/144)^(1/2)-5/12)/(-3) or m = ((8665/144)^(1/2)+5/12)/3

m in { ((8665/144)^(1/2)-5/12)/(-3), ((8665/144)^(1/2)+5/12)/3} 

m in { ((8665/144)^(1/2)-5/12)/(-3), ((8665/144)^(1/2)+5/12)/3 }

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