(2x-9)^2/3=(x-4)^1/3

Solution for (2x-9)^2/3=(x-4)^1/3 equation:

x in (-oo:+oo)

((2*x-9)^2)/3 = ((x-4)^1)/3 // - ((x-4)^1)/3

((2*x-9)^2)/3-(((x-4)^1)/3) = 0

((2*x-9)^2)/3-((x-4)/3) = 0

((2*x-9)^2)/3+(-1*(x-4))/3 = 0

(2*x-9)^2-1*(x-4) = 0

4*x^2-37*x+85 = 0

4*x^2-37*x+85 = 0

4*x^2-37*x+85 = 0

DELTA = (-37)^2-(4*4*85)

DELTA = 9

DELTA > 0

x = (9^(1/2)+37)/(2*4) or x = (37-9^(1/2))/(2*4)

x = 5 or x = 17/4

(x-17/4)*(x-5) = 0

((x-17/4)*(x-5))/3 = 0

((x-17/4)*(x-5))/3 = 0 // * 3

(x-17/4)*(x-5) = 0

( x-17/4 )

x-17/4 = 0 // + 17/4

x = 17/4

( x-5 )

x-5 = 0 // + 5

x = 5

x in { 17/4, 5 }