(2x^2-2x-24)(1/x-1)

Solution for (2x^2-2x-24)(1/x-1) equation:

D( x )

x = 0

x = 0

x = 0

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

(2*x^2-(2*x)-24)*(1/x-1) = 0

(2*x^2-2*x-24)*(1/x-1) = 0

(2*x^2-2*x-24)*(x^-1-1) = 0

2*x^2-2*x-24 = 0

2*(x^2-x-12) = 0

x^2-x-12 = 0

DELTA = (-1)^2-(-12*1*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)+1)/(1*2) or x = (1-49^(1/2))/(1*2)

x = 4 or x = -3

2*(x+3)*(x-4) = 0

2*(x+3)*(x-4)*(x^-1-1) = 0

( 2 )

2 = 0

x belongs to the empty set

( x+3 )

x+3 = 0 // - 3

x = -3

( x-4 )

x-4 = 0 // + 4

x = 4

( x^-1-1 )

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

x^-1 = 1

-1 < 0

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

1 = 1*x^1 // : 1

1 = x^1

x = 1

x in { -3, 4, 1 }