1/x+1/(x+120)=1/90

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Solution for 1/x+1/(x+120)=1/90 equation: 


D( x )

x+120 = 0

x = 0

x+120 = 0

x+120 = 0

x+120 = 0 // - 120

x = -120

x = 0

x = 0

x in (-oo:-120) U (-120:0) U (0:+oo)

1/(x+120)+1/x = 1/90 // - 1/90

1/(x+120)+1/x-(1/90) = 0

1/(x+120)+1/x-1/90 = 0

(1*90*x)/(90*x*(x+120))+(1*90*(x+120))/(90*x*(x+120))+(-1*x*(x+120))/(90*x*(x+120)) = 0

1*90*(x+120)-1*x*(x+120)+1*90*x = 0

180*x-x^2-120*x+10800 = 0

60*x-x^2+10800 = 0

60*x-x^2+10800 = 0

60*x-x^2+10800 = 0

DELTA = 60^2-(-1*4*10800)

DELTA = 46800

DELTA > 0

x = (46800^(1/2)-60)/(-1*2) or x = (-46800^(1/2)-60)/(-1*2)

x = (60*13^(1/2)-60)/(-2) or x = (-60*13^(1/2)-60)/(-2)

(x-((60*13^(1/2)-60)/(-2)))*(x-((-60*13^(1/2)-60)/(-2))) = 0

((x-((60*13^(1/2)-60)/(-2)))*(x-((-60*13^(1/2)-60)/(-2))))/(90*x*(x+120)) = 0

((x-((60*13^(1/2)-60)/(-2)))*(x-((-60*13^(1/2)-60)/(-2))))/(90*x*(x+120)) = 0 // * 90*x*(x+120)

(x-((60*13^(1/2)-60)/(-2)))*(x-((-60*13^(1/2)-60)/(-2))) = 0

( x-((-60*13^(1/2)-60)/(-2)) )

x-((-60*13^(1/2)-60)/(-2)) = 0 // + (-60*13^(1/2)-60)/(-2)

x = (-60*13^(1/2)-60)/(-2)

( x-((60*13^(1/2)-60)/(-2)) )

x-((60*13^(1/2)-60)/(-2)) = 0 // + (60*13^(1/2)-60)/(-2)

x = (60*13^(1/2)-60)/(-2)

x in { (-60*13^(1/2)-60)/(-2), (60*13^(1/2)-60)/(-2) }

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