27x^5+215x^(5/2)-8=0

Solution for 27x^5+215x^(5/2)-8=0 equation:

D( x )

x < 0

x < 0

x in <0:+oo)

27*x^5+215*x^(5/2)-8 = 0

t_1 = x^(5/2)

27*t_1^2+215*t_1^1-8 = 0

27*t_1^2+215*t_1-8 = 0

DELTA = 215^2-(-8*4*27)

DELTA = 47089

DELTA > 0

t_1 = (47089^(1/2)-215)/(2*27) or t_1 = (-47089^(1/2)-215)/(2*27)

t_1 = 1/27 or t_1 = -8

t_1 = -8

x^(5/2)+8 = 0

1*x^(5/2) = -8 // : 1

x^(5/2) = -8

x^(5/2) = -8 // ^ 2

x^5 = 64 // ^ 1/5

x = 2*2^(1/5)

t_1 = 1/27

x^(5/2)-1/27 = 0

1*x^(5/2) = 1/27 // : 1

x^(5/2) = 1/27

x^(5/2) = 1/27 // ^ 2

x^5 = 1/729 // ^ 1/5

x = (1/729)^(1/5)

x in { 2*2^(1/5), (1/729)^(1/5) }