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

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


D( z )

z+4 = 0

z+4 = 0

z+4 = 0

z+4 = 0 // - 4

z = -4

z in (-oo:-4) U (-4:+oo)

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

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

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

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

69-81*z*(z+4) = 0

69-81*z^2-324*z = 0

69-81*z^2-324*z = 0

3*(23-27*z^2-108*z) = 0

23-27*z^2-108*z = 0

DELTA = (-108)^2-(-27*4*23)

DELTA = 14148

DELTA > 0

z = (14148^(1/2)+108)/(-27*2) or z = (108-14148^(1/2))/(-27*2)

z = (6*393^(1/2)+108)/(-54) or z = (108-6*393^(1/2))/(-54)

3*(z-((6*393^(1/2)+108)/(-54)))*(z-((108-6*393^(1/2))/(-54))) = 0

(3*(z-((6*393^(1/2)+108)/(-54)))*(z-((108-6*393^(1/2))/(-54))))/(z+4) = 0

(3*(z-((6*393^(1/2)+108)/(-54)))*(z-((108-6*393^(1/2))/(-54))))/(z+4) = 0 // * z+4

3*(z-((6*393^(1/2)+108)/(-54)))*(z-((108-6*393^(1/2))/(-54))) = 0

( z-((108-6*393^(1/2))/(-54)) )

z-((108-6*393^(1/2))/(-54)) = 0 // + (108-6*393^(1/2))/(-54)

z = (108-6*393^(1/2))/(-54)

( z-((6*393^(1/2)+108)/(-54)) )

z-((6*393^(1/2)+108)/(-54)) = 0 // + (6*393^(1/2)+108)/(-54)

z = (6*393^(1/2)+108)/(-54)

z in { (108-6*393^(1/2))/(-54), (6*393^(1/2)+108)/(-54) }

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