6x^(3/2)=11x^(3/4)-4

Solution for 6x^(3/2)=11x^(3/4)-4 equation:

D( x )

x < 0

x < 0

x in <0:+oo)

6*x^(3/2) = 11*x^(3/4)-4 // - 11*x^(3/4)-4

6*x^(3/2)-(11*x^(3/4))+4 = 0

6*x^(3/2)-11*x^(3/4)+4 = 0

t_1 = x^(3/4)

6*t_1^2-11*t_1^1+4 = 0

6*t_1^2-11*t_1+4 = 0

DELTA = (-11)^2-(4*4*6)

DELTA = 25

DELTA > 0

t_1 = (25^(1/2)+11)/(2*6) or t_1 = (11-25^(1/2))/(2*6)

t_1 = 4/3 or t_1 = 1/2

t_1 = 1/2

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

1*x^(3/4) = 1/2 // : 1

x^(3/4) = 1/2

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

x^3 = 1/16 // ^ 1/3

x = (1/16)^(1/3)

t_1 = 4/3

x^(3/4)-4/3 = 0

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

x^(3/4) = 4/3

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

x^3 = 256/81 // ^ 1/3

x = (256/81)^(1/3)

x in { (1/16)^(1/3), (256/81)^(1/3) }