69/z+4=162/2z

Solution for 69/z+4=162/2z equation:

D( z )

z = 0

z = 0

z = 0

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

69/z+4 = (162/2)*z // - (162/2)*z

69/z-((162/2)*z)+4 = 0

69/z-81*z+4 = 0

69*z^-1-81*z^1+4*z^0 = 0

(4*z^1-81*z^2+69*z^0)/(z^1) = 0 // * z^2

z^1*(4*z^1-81*z^2+69*z^0) = 0

z^1

4*z-81*z^2+69 = 0

4*z-81*z^2+69 = 0

DELTA = 4^2-(-81*4*69)

DELTA = 22372

DELTA > 0

z = (22372^(1/2)-4)/(-81*2) or z = (-22372^(1/2)-4)/(-81*2)

z = (2*5593^(1/2)-4)/(-162) or z = (-2*5593^(1/2)-4)/(-162)

z in { (2*5593^(1/2)-4)/(-162), (-2*5593^(1/2)-4)/(-162)} 

z in { (2*5593^(1/2)-4)/(-162), (-2*5593^(1/2)-4)/(-162) }