(3/z)-(4/5z)=1/10

Solution for (3/z)-(4/5z)=1/10 equation:

D( z )

z = 0

z = 0

z = 0

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

3/z-((4/5)*z) = 1/10 // - 1/10

3/z-((4/5)*z)-(1/10) = 0

(-4/5)*z+3/z-1/10 = 0

3*z^-1-4/5*z^1-1/10*z^0 = 0

(3*z^0-4/5*z^2-1/10*z^1)/(z^1) = 0 // * z^2

z^1*(3*z^0-4/5*z^2-1/10*z^1) = 0

z^1

(-4/5)*z^2+(-1/10)*z+3 = 0

(-4/5)*z^2+(-1/10)*z+3 = 0

DELTA = (-1/10)^2-(3*4*(-4/5))

DELTA = 961/100

DELTA > 0

z = ((961/100)^(1/2)-(-1/10))/(2*(-4/5)) or z = (-(-1/10)-(961/100)^(1/2))/(2*(-4/5))

z = -2 or z = 15/8

z in { -2, 15/8} 

z in { -2, 15/8 }