8x-64x^(-1/2)=0

Solution for 8x-64x^(-1/2)=0 equation:

D( x )

x < 0

x = 0

x < 0

x = 0

x = 0

x in (0:+oo)

8*x-(64*x^(-1/2)) = 0

8*x-64*x^(-1/2) = 0

t_1 = x^(1/2)

8*t_1^2-64*t_1^-1 = 0

(8*t_1^3-64*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(8*t_1^3-64*t_1^0) = 0

t_1^1

8*t_1^3-64 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64 }

1

t_1 = 1

8*t_1^3-64 = -56

1

-1

t_1 = -1

8*t_1^3-64 = -72

-1

2

t_1 = 2

8*t_1^3-64 = 0

2

t_1-2

8*t_1^2+16*t_1+32

8*t_1^3-64

t_1-2

16*t_1^2-8*t_1^3

16*t_1^2-64

32*t_1-16*t_1^2

32*t_1-64

64-32*t_1

0

8*t_1^2+16*t_1+32 = 0

DELTA = 16^2-(4*8*32)

DELTA = -768

DELTA < 0

t_1 in { 2} 

t_1 = 2

x^(1/2)-2 = 0

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

x^(1/2) = 2

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

x = 4

x = 4