x^(3/2)=8x^(3/4)-15

Solution for x^(3/2)=8x^(3/4)-15 equation:

D( x )

x < 0

x < 0

x in <0:+oo)

x^(3/2) = 8*x^(3/4)-15 // - 8*x^(3/4)-15

x^(3/2)-(8*x^(3/4))+15 = 0

x^(3/2)-8*x^(3/4)+15 = 0

t_1 = x^(3/4)

1*t_1^2-8*t_1^1+15 = 0

t_1^2-8*t_1+15 = 0

DELTA = (-8)^2-(1*4*15)

DELTA = 4

DELTA > 0

t_1 = (4^(1/2)+8)/(1*2) or t_1 = (8-4^(1/2))/(1*2)

t_1 = 5 or t_1 = 3

t_1 = 3

x^(3/4)-3 = 0

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

x^(3/4) = 3

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

x^3 = 81 // ^ 1/3

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