6x^5*e^7x-8x^6*e^8x/x^4

Solution for 6x^5*e^7x-8x^6*e^8x/x^4 equation:

D( x )

x^4 = 0

x^4 = 0

x^4 = 0

1*x^4 = 0 // : 1

x^4 = 0

x = 0

x in (-oo:0) U (0:+oo)

6*e^7*x*x^5-((8*e^8*x*x^6)/(x^4)) = 0

6*e^7*x*x^5-8*e^8*x^3 = 0

6*e^7*x^6-8*e^8*x^3 = 0

t_1 = x^3

6*e^7*t_1^2-8*e^8*t_1^1 = 0

6*e^7*t_1^2-8*e^8*t_1 = 0

DELTA = (-8*e^8)^2-(0*4*6*e^7)

DELTA = 64*e^16

DELTA = 568711078.4708096

DELTA > 0

t_1 = ((64*e^16)^(1/2)-(-8*e^8))/(2*6*e^7) or t_1 = (-(-8*e^8)-(64*e^16)^(1/2))/(2*6*e^7)

t_1 = (4*e)/3 or t_1 = 0

t_1 = 0

x^3+0 = 0

x^3 = 0

1*x^3 = 0 // : 1

x^3 = 0

x = 0

t_1 = (4*e)/3

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

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

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

x^3 = 4/3*e

x^3 = 4/3*e // ^ 1/3

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

x in { 0} 

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