(3z-2)^2/5=(8z)^1/5

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Solution for (3z-2)^2/5=(8z)^1/5 equation: 


z in (-oo:+oo)

((3*z-2)^2)/5 = ((8*z)^1)/5 // - ((8*z)^1)/5

((3*z-2)^2)/5-(((8*z)^1)/5) = 0

((3*z-2)^2)/5+(-8/5)*z = 0

((3*z-2)^2)/5+(-8*z)/5 = 0

(3*z-2)^2-8*z = 0

9*z^2-20*z+4 = 0

9*z^2-20*z+4 = 0

9*z^2-20*z+4 = 0

DELTA = (-20)^2-(4*4*9)

DELTA = 256

DELTA > 0

z = (256^(1/2)+20)/(2*9) or z = (20-256^(1/2))/(2*9)

z = 2 or z = 2/9

(z-2/9)*(z-2) = 0

((z-2/9)*(z-2))/5 = 0

((z-2/9)*(z-2))/5 = 0 // * 5

(z-2/9)*(z-2) = 0

( z-2/9 )

z-2/9 = 0 // + 2/9

z = 2/9

( z-2 )

z-2 = 0 // + 2

z = 2

z in { 2/9, 2 }

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