(3x-4)^2/3=(16x)^1/3

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Solution for (3x-4)^2/3=(16x)^1/3 equation:


x in (-oo:+oo)

((3*x-4)^2)/3 = ((16*x)^1)/3 // - ((16*x)^1)/3

((3*x-4)^2)/3-(((16*x)^1)/3) = 0

((3*x-4)^2)/3+(-16/3)*x = 0

((3*x-4)^2)/3+(-16*x)/3 = 0

(3*x-4)^2-16*x = 0

9*x^2-40*x+16 = 0

9*x^2-40*x+16 = 0

9*x^2-40*x+16 = 0

DELTA = (-40)^2-(4*9*16)

DELTA = 1024

DELTA > 0

x = (1024^(1/2)+40)/(2*9) or x = (40-1024^(1/2))/(2*9)

x = 4 or x = 4/9

(x-4/9)*(x-4) = 0

((x-4/9)*(x-4))/3 = 0

((x-4/9)*(x-4))/3 = 0 // * 3

(x-4/9)*(x-4) = 0

( x-4/9 )

x-4/9 = 0 // + 4/9

x = 4/9

( x-4 )

x-4 = 0 // + 4

x = 4

x in { 4/9, 4 }

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