20/x^2-4x+7=x+2

Solution for 20/x^2-4x+7=x+2 equation:

D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

20/(x^2)-(4*x)+7 = x+2 // - x+2

20/(x^2)-(4*x)-x-2+7 = 0

20/(x^2)-4*x-x-2+7 = 0

20*x^-2-5*x^1+5*x^0 = 0

(5*x^2-5*x^3+20*x^0)/(x^2) = 0 // * x^4

x^2*(5*x^2-5*x^3+20*x^0) = 0

x^2

5*x^2-5*x^3+20 = 0

{ 1, -1, 2, -2, 4, -4, 5, -5, 10, -10, 20, -20 }

1

x = 1

5*x^2-5*x^3+20 = 20

1

-1

x = -1

5*x^2-5*x^3+20 = 30

-1

2

x = 2

5*x^2-5*x^3+20 = 0

2

x-2

-5*x^2-5*x-10

5*x^2-5*x^3+20

x-2

5*x^3-10*x^2

20-5*x^2

5*x^2-10*x

20-10*x

10*x-20

0

-5*x^2-5*x-10 = 0

DELTA = (-5)^2-(-10*(-5)*4)

DELTA = -175

DELTA < 0

x in { 2} 

x = 2