(27x^5+9x^4-18x^3)/(9x^2)

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Solution for (27x^5+9x^4-18x^3)/(9x^2) equation:


D( x )

9*x^2 = 0

9*x^2 = 0

9*x^2 = 0

9*x^2 = 0 // : 9

x^2 = 0

x = 0

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

(27*x^5+9*x^4-(18*x^3))/(9*x^2) = 0

(27*x^5+9*x^4-18*x^3)/(9*x^2) = 0

27*x^5+9*x^4-18*x^3 = 0

9*x^3*(3*x^2+x-2) = 0

3*x^2+x-2 = 0

DELTA = 1^2-(-2*3*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)-1)/(2*3) or x = (-25^(1/2)-1)/(2*3)

x = 2/3 or x = -1

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

(9*x^3*(x+1)*(x-2/3))/(9*x^2) = 0

( 9*x^3 )

9*x^3 = 0 // : 9

x^3 = 0

x = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-2/3 )

x-2/3 = 0 // + 2/3

x = 2/3

x in { 0}

x in { -1, 2/3 }

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