(3/z)-(1/5z)=5/6

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Solution for (3/z)-(1/5z)=5/6 equation: 


D( z )

z = 0

z = 0

z = 0

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

3/z-((1/5)*z) = 5/6 // - 5/6

3/z-((1/5)*z)-(5/6) = 0

(-1/5)*z+3/z-5/6 = 0

3*z^-1-1/5*z^1-5/6*z^0 = 0

(3*z^0-1/5*z^2-5/6*z^1)/(z^1) = 0 // * z^2

z^1*(3*z^0-1/5*z^2-5/6*z^1) = 0

z^1

(-1/5)*z^2+(-5/6)*z+3 = 0

(-1/5)*z^2+(-5/6)*z+3 = 0

DELTA = (-5/6)^2-(3*4*(-1/5))

DELTA = 557/180

DELTA > 0

z = ((557/180)^(1/2)-(-5/6))/(2*(-1/5)) or z = (-(-5/6)-(557/180)^(1/2))/(2*(-1/5))

z = -5/2*((557/180)^(1/2)+5/6) or z = -5/2*(5/6-(557/180)^(1/2))

z in { -5/2*((557/180)^(1/2)+5/6), -5/2*(5/6-(557/180)^(1/2))} 

z in { -5/2*((557/180)^(1/2)+5/6), -5/2*(5/6-(557/180)^(1/2)) }

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