(50/x)-(50/(x-5))=-1/2

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Solution for (50/x)-(50/(x-5))=-1/2 equation:


D( x )

x-5 = 0

x = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x = 0

x = 0

x in (-oo:0) U (0:5) U (5:+oo)

50/x-(50/(x-5)) = -1/2 // + -1/2

50/x-(50/(x-5))-(-1/2) = 0

50/x-50*(x-5)^-1+1/2 = 0

50/x-50/(x-5)+1/2 = 0

(-50*2*x)/(2*x*(x-5))+(2*50*(x-5))/(2*x*(x-5))+(1*x*(x-5))/(2*x*(x-5)) = 0

2*50*(x-5)+1*x*(x-5)-50*2*x = 0

x^2-5*x-500 = 0

x^2-5*x-500 = 0

x^2-5*x-500 = 0

DELTA = (-5)^2-(-500*1*4)

DELTA = 2025

DELTA > 0

x = (2025^(1/2)+5)/(1*2) or x = (5-2025^(1/2))/(1*2)

x = 25 or x = -20

(x+20)*(x-25) = 0

((x+20)*(x-25))/(2*x*(x-5)) = 0

((x+20)*(x-25))/(2*x*(x-5)) = 0 // * 2*x*(x-5)

(x+20)*(x-25) = 0

( x+20 )

x+20 = 0 // - 20

x = -20

( x-25 )

x-25 = 0 // + 25

x = 25

x in { -20, 25 }

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