3/4z=-7/z-1/7+6

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Solution for 3/4z=-7/z-1/7+6 equation: 


D( z )

z = 0

z = 0

z = 0

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

(3/4)*z = 6-7/z-(1/7) // - 6-7/z-(1/7)

(3/4)*z-(-7/z)+1/7-6 = 0

(3/4)*z+7*z^-1+1/7-6 = 0

3/4*z^1+7*z^-1-41/7*z^0 = 0

(3/4*z^2-41/7*z^1+7*z^0)/(z^1) = 0 // * z^2

z^1*(3/4*z^2-41/7*z^1+7*z^0) = 0

z^1

(3/4)*z^2+(-41/7)*z+7 = 0

(3/4)*z^2+(-41/7)*z+7 = 0

DELTA = (-41/7)^2-(4*7*(3/4))

DELTA = 652/49

DELTA > 0

z = ((652/49)^(1/2)-(-41/7))/(2*(3/4)) or z = (-(-41/7)-(652/49)^(1/2))/(2*(3/4))

z = 2/3*((652/49)^(1/2)+41/7) or z = 2/3*(41/7-(652/49)^(1/2))

z in { 2/3*(41/7-(652/49)^(1/2)), 2/3*((652/49)^(1/2)+41/7)} 

z in { 2/3*(41/7-(652/49)^(1/2)), 2/3*((652/49)^(1/2)+41/7) }

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