(27x5+9x4-18x3)/9x2

Solution for (27x5+9x4-18x3)/9x2 equation:

x in (-oo:+oo)

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

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

(x^2*(27*x^5+9*x^4-18*x^3))/9 = 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^2*x^3*(x+1)*(x-2/3))/9 = 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^2 )

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in { 0, -1, 2/3, 0 }