(5/x)^2-3(5/x)=4

Solution for (5/x)^2-3(5/x)=4 equation:

D( x )

x = 0

x = 0

x = 0

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

(5/x)^2-(3*(5/x)) = 4 // - 4

(5/x)^2-(3*(5/x))-4 = 0

(5/x)^2-15*x^-1-4 = 0

25*x^-2-15*x^-1-4 = 0

t_1 = x^-1

25*t_1^2-15*t_1^1-4 = 0

25*t_1^2-15*t_1-4 = 0

DELTA = (-15)^2-(-4*4*25)

DELTA = 625

DELTA > 0

t_1 = (625^(1/2)+15)/(2*25) or t_1 = (15-625^(1/2))/(2*25)

t_1 = 4/5 or t_1 = -1/5

t_1 = -1/5

x^-1+1/5 = 0

1*x^-1 = -1/5 // : 1

x^-1 = -1/5

-1 < 0

1/(x^1) = -1/5 // * x^1

1 = -1/5*x^1 // : -1/5

-5 = x^1

x = -5

t_1 = 4/5

x^-1-4/5 = 0

1*x^-1 = 4/5 // : 1

x^-1 = 4/5

-1 < 0

1/(x^1) = 4/5 // * x^1

1 = 4/5*x^1 // : 4/5

5/4 = x^1

x = 5/4

x in { -5, 5/4 }