(4z+7)/(z-19)=415/(5z-95)

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Solution for (4z+7)/(z-19)=415/(5z-95) equation: 


D( z )

z-19 = 0

5*z-95 = 0

z-19 = 0

z-19 = 0

z-19 = 0 // + 19

z = 19

5*z-95 = 0

5*z-95 = 0

5*z-95 = 0 // + 95

5*z = 95 // : 5

z = 95/5

z = 19

z in (-oo:19) U (19:+oo)

(4*z+7)/(z-19) = 415/(5*z-95) // - 415/(5*z-95)

(4*z+7)/(z-19)-(415/(5*z-95)) = 0

(4*z+7)/(z-19)-415*(5*z-95)^-1 = 0

(4*z+7)/(z-19)-415/(5*z-95) = 0

((4*z+7)*(5*z-95))/((z-19)*(5*z-95))+(-415*(z-19))/((z-19)*(5*z-95)) = 0

(4*z+7)*(5*z-95)-415*(z-19) = 0

20*z^2-760*z+7220 = 0

20*z^2-760*z+7220 = 0

20*(z^2-38*z+361) = 0

z^2-38*z+361 = 0

DELTA = (-38)^2-(1*4*361)

DELTA = 0

z = 38/(1*2)

z = 19 or z = 19

20*(z-19)^2 = 0

(20*(z-19)^2)/((z-19)*(5*z-95)) = 0

(20*(z-19)^2)/((z-19)*(5*z-95)) = 0 // * (z-19)*(5*z-95)

20*(z-19)^2 = 0

z-19 = 0 // + 19

z = 19

z in { 19} 

z belongs to the empty set

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