(z-3)^2/3=(13z-81)^1/3

Solution for (z-3)^2/3=(13z-81)^1/3 equation:

z in (-oo:+oo)

((z-3)^2)/3 = ((13*z-81)^1)/3 // - ((13*z-81)^1)/3

((z-3)^2)/3-(((13*z-81)^1)/3) = 0

((z-3)^2)/3-((13*z-81)/3) = 0

((z-3)^2)/3+(-1*(13*z-81))/3 = 0

(z-3)^2-1*(13*z-81) = 0

z^2-19*z+90 = 0

z^2-19*z+90 = 0

z^2-19*z+90 = 0

DELTA = (-19)^2-(1*4*90)

DELTA = 1

DELTA > 0

z = (1^(1/2)+19)/(1*2) or z = (19-1^(1/2))/(1*2)

z = 10 or z = 9

(z-9)*(z-10) = 0

((z-9)*(z-10))/3 = 0

((z-9)*(z-10))/3 = 0 // * 3

(z-9)*(z-10) = 0

( z-10 )

z-10 = 0 // + 10

z = 10

( z-9 )

z-9 = 0 // + 9

z = 9

z in { 10, 9 }