(2x-4)/39=24/(x-6)

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Solution for (2x-4)/39=24/(x-6) equation: 


D( x )

x-6 = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

x in (-oo:6) U (6:+oo)

(2*x-4)/39 = 24/(x-6) // - 24/(x-6)

(2*x-4)/39-(24/(x-6)) = 0

(2*x-4)/39-24*(x-6)^-1 = 0

(2*x-4)/39-24/(x-6) = 0

((2*x-4)*(x-6))/(39*(x-6))+(-24*39)/(39*(x-6)) = 0

(2*x-4)*(x-6)-24*39 = 0

2*x^2-16*x-912 = 0

2*x^2-16*x-912 = 0

2*(x^2-8*x-456) = 0

x^2-8*x-456 = 0

DELTA = (-8)^2-(-456*1*4)

DELTA = 1888

DELTA > 0

x = (1888^(1/2)+8)/(1*2) or x = (8-1888^(1/2))/(1*2)

x = (4*118^(1/2)+8)/2 or x = (8-4*118^(1/2))/2

2*(x-((8-4*118^(1/2))/2))*(x-((4*118^(1/2)+8)/2)) = 0

(2*(x-((8-4*118^(1/2))/2))*(x-((4*118^(1/2)+8)/2)))/(39*(x-6)) = 0

(2*(x-((8-4*118^(1/2))/2))*(x-((4*118^(1/2)+8)/2)))/(39*(x-6)) = 0 // * 39*(x-6)

2*(x-((8-4*118^(1/2))/2))*(x-((4*118^(1/2)+8)/2)) = 0

( x-((4*118^(1/2)+8)/2) )

x-((4*118^(1/2)+8)/2) = 0 // + (4*118^(1/2)+8)/2

x = (4*118^(1/2)+8)/2

( x-((8-4*118^(1/2))/2) )

x-((8-4*118^(1/2))/2) = 0 // + (8-4*118^(1/2))/2

x = (8-4*118^(1/2))/2

x in { (4*118^(1/2)+8)/2, (8-4*118^(1/2))/2 }

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