(1+8/x)(1-4/x)=18/25

Solution for (1+8/x)(1-4/x)=18/25 equation:

D( x )

x = 0

x = 0

x = 0

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

(8/x+1)*(1-(4/x)) = 18/25 // - 18/25

(8/x+1)*(1-(4/x))-(18/25) = 0

(8/x+1)*(1-4*x^-1)-18/25 = 0

(8*x^-1+1)*(1-4*x^-1)-18/25 = 0

(25*(8*x^-1+1)*(1-4*x^-1))/25-18/25 = 0

25*(8*x^-1+1)*(1-4*x^-1)-18 = 0

100*x^-1-800*x^-2+7 = 0

100*x^-1-800*x^-2+7 = 0

100*x^-1-800*x^-2+7*x^0 = 0

(7*x^2+100*x^1-800*x^0)/(x^2) = 0 // * x^4

x^2*(7*x^2+100*x^1-800*x^0) = 0

x^2

7*x^2+100*x-800 = 0

7*x^2+100*x-800 = 0

DELTA = 100^2-(-800*4*7)

DELTA = 32400

DELTA > 0

x = (32400^(1/2)-100)/(2*7) or x = (-32400^(1/2)-100)/(2*7)

x = 40/7 or x = -20

x in { -20, 40/7} 

(x+20)*(x-40/7) = 0

((x+20)*(x-40/7))/25 = 0

((x+20)*(x-40/7))/25 = 0 // * 25

(x+20)*(x-40/7) = 0

( x+20 )

x+20 = 0 // - 20

x = -20

( x-40/7 )

x-40/7 = 0 // + 40/7

x = 40/7

x in { -20, 40/7 }