2/5(x)=1/x-4

Solution for 2/5(x)=1/x-4 equation:

D( x )

x = 0

x = 0

x = 0

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

(2/5)*x = 1/x-4 // - 1/x-4

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

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

2/5*x^1-1*x^-1+4*x^0 = 0

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

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

x^1

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

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

DELTA = 4^2-(-1*4*(2/5))

DELTA = 88/5

DELTA > 0

x = ((88/5)^(1/2)-4)/(2*(2/5)) or x = (-(88/5)^(1/2)-4)/(2*(2/5))

x = 5/4*((88/5)^(1/2)-4) or x = -5/4*((88/5)^(1/2)+4)

x in { -5/4*((88/5)^(1/2)+4), 5/4*((88/5)^(1/2)-4)} 

x in { -5/4*((88/5)^(1/2)+4), 5/4*((88/5)^(1/2)-4) }