x^(3/2)=5x^(3/4)-4

Solution for x^(3/2)=5x^(3/4)-4 equation:

D( x )

x < 0

x < 0

x in <0:+oo)

x^(3/2) = 5*x^(3/4)-4 // - 5*x^(3/4)-4

x^(3/2)-(5*x^(3/4))+4 = 0

x^(3/2)-5*x^(3/4)+4 = 0

t_1 = x^(3/4)

1*t_1^2-5*t_1^1+4 = 0

t_1^2-5*t_1+4 = 0

DELTA = (-5)^2-(1*4*4)

DELTA = 9

DELTA > 0

t_1 = (9^(1/2)+5)/(1*2) or t_1 = (5-9^(1/2))/(1*2)

t_1 = 4 or t_1 = 1

t_1 = 1

x^(3/4)-1 = 0

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

x^(3/4) = 1

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

x^3 = 1 // ^ 1/3

x = 1

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)

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