(X3-13x2+40x+18)/(x-7)

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Solution for (X3-13x2+40x+18)/(x-7) equation: 


D( x )

x-7 = 0

x-7 = 0

x-7 = 0

x-7 = 0 // + 7

x = 7

x in (-oo:7) U (7:+oo)

(X^3-(13*x^2)+40*x+18)/(x-7) = 0

(X^3-13*x^2+40*x+18)/(x-7) = 0

X^3-13*x^2+40*x+18 = 0

DELTA = 40^2-(-13*4*(X^3+18))

DELTA = 52*(X^3+18)+1600

52*(X^3+18)+1600 = 0

52*(X^3+18)+1600 = 0

52*X^3+2536 = 0

52*X^3+2536 = 0

52*X^3 = -2536 // : 52

X^3 = -634/13

X^3 = -634/13 // ^ 1/3

X = -(634/13)^(1/3)

DELTA = 0  <=>  t_2 = -(634/13)^(1/3)

x = -40/(-13*2) i X = -(634/13)^(1/3)

x = 20/13 i X = -(634/13)^(1/3)

( x = ((52*(X^3+18)+1600)^(1/2)-40)/(-13*2) or x = (-(52*(X^3+18)+1600)^(1/2)-40)/(-13*2) ) i X > -(634/13)^(1/3)

( x = ((52*(X^3+18)+1600)^(1/2)-40)/(-26) or x = ((52*(X^3+18)+1600)^(1/2)+40)/26 ) i X > -(634/13)^(1/3)

X+(634/13)^(1/3) > 0

X+(634/13)^(1/3) > 0 // - (634/13)^(1/3)

X > -(634/13)^(1/3)

x in { 20/13, ((52*(X^3+18)+1600)^(1/2)-40)/(-26), ((52*(X^3+18)+1600)^(1/2)+40)/26 }

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