x^(3/2)=9x^(3/4)-20

Solution for x^(3/2)=9x^(3/4)-20 equation:

D( x )

x < 0

x < 0

x in <0:+oo)

x^(3/2) = 9*x^(3/4)-20 // - 9*x^(3/4)-20

x^(3/2)-(9*x^(3/4))+20 = 0

x^(3/2)-9*x^(3/4)+20 = 0

t_1 = x^(3/4)

1*t_1^2-9*t_1^1+20 = 0

t_1^2-9*t_1+20 = 0

DELTA = (-9)^2-(1*4*20)

DELTA = 1

DELTA > 0

t_1 = (1^(1/2)+9)/(1*2) or t_1 = (9-1^(1/2))/(1*2)

t_1 = 5 or t_1 = 4

t_1 = 4

x^(3/4)-4 = 0

1*x^(3/4) = 4 // : 1

x^(3/4) = 4

x^(3/4) = 4 // ^ 4

x^3 = 256 // ^ 1/3

x = 4*4^(1/3)

t_1 = 5

x^(3/4)-5 = 0

1*x^(3/4) = 5 // : 1

x^(3/4) = 5

x^(3/4) = 5 // ^ 4

x^3 = 625 // ^ 1/3

x = 5*5^(1/3)

x in { 4*4^(1/3), 5*5^(1/3) }