(x-20/x)^2-7(x-20/x)-8=0

Solution for (x-20/x)^2-7(x-20/x)-8=0 equation:

D( x )

x = 0

x = 0

x = 0

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

(x-(20/x))^2-(7*(x-(20/x)))-8 = 0

(x-20*x^-1)^2-7*(x-20*x^-1)-8 = 0

(x-20*x^-1)^2-7*(x-20*x^-1)-8 = 0

x^2-7*x+140*x^-1+400*x^-2-40-8 = 0

x^2-7*x+140*x^-1+400*x^-2-48 = 0

x^2-7*x+140*x^-1+400*x^-2-48 = 0

1*x^2-7*x^1+140*x^-1+400*x^-2-48*x^0 = 0

(1*x^4-7*x^3-48*x^2+140*x^1+400*x^0)/(x^2) = 0 // * x^4

x^2*(1*x^4-7*x^3-48*x^2+140*x^1+400*x^0) = 0

x^2

x^4-7*x^3-48*x^2+140*x+400 = 0

{ 1, -1, 2, -2, 4, -4, 5, -5, 8, -8, 10, -10, 16, -16, 20, -20, 25, -25, 40, -40, 50, -50, 80, -80, 100, -100, 200, -200, 400, -400 }

1

x = 1

x^4-7*x^3-48*x^2+140*x+400 = 486

1

-1

x = -1

x^4-7*x^3-48*x^2+140*x+400 = 220

-1

2

x = 2

x^4-7*x^3-48*x^2+140*x+400 = 448

2

-2

x = -2

x^4-7*x^3-48*x^2+140*x+400 = 0

-2

x+2

x^3-9*x^2-30*x+200

x^4-7*x^3-48*x^2+140*x+400

x+2

-x^4-2*x^3

140*x-9*x^3-48*x^2+400

9*x^3+18*x^2

140*x-30*x^2+400

30*x^2+60*x

200*x+400

-200*x-400

0

x^3-9*x^2-30*x+200 = 0

{ 1, -1, 2, -2, 4, -4, 5, -5, 8, -8, 10, -10, 20, -20, 25, -25, 40, -40, 50, -50, 100, -100, 200, -200 }

1

x = 1

x^3-9*x^2-30*x+200 = 162

1

-1

x = -1

x^3-9*x^2-30*x+200 = 220

-1

2

x = 2

x^3-9*x^2-30*x+200 = 112

2

-2

x = -2

x^3-9*x^2-30*x+200 = 216

-2

4

x = 4

x^3-9*x^2-30*x+200 = 0

4

x-4

x^2-5*x-50

x^3-9*x^2-30*x+200

x-4

4*x^2-x^3

200-5*x^2-30*x

5*x^2-20*x

200-50*x

50*x-200

0

x^2-5*x-50 = 0

DELTA = (-5)^2-(-50*1*4)

DELTA = 225

DELTA > 0

x = (225^(1/2)+5)/(1*2) or x = (5-225^(1/2))/(1*2)

x = 10 or x = -5

x in { -5, 10, -2, 4} 

(x+5)*(x-10)*(x+2)*(x-4) = 0

(x+5)*(x-10)*(x+2)*(x-4) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x+5 )

x+5 = 0 // - 5

x = -5

( x-10 )

x-10 = 0 // + 10

x = 10

( x-4 )

x-4 = 0 // + 4

x = 4

x in { -2, -5, 10, 4 }