(6x^3-10x2)/(3x^3-2x^2-5x)=0

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Solution for (6x^3-10x2)/(3x^3-2x^2-5x)=0 equation:


D( x )

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

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

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

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

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

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

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

DELTA = (-2)^2-(-5*3*4)

DELTA = 64

DELTA > 0

x = (64^(1/2)+2)/(2*3) or x = (2-64^(1/2))/(2*3)

x = 5/3 or x = -1

x = 0

x = 0

x in (-oo:-1) U (-1:0) U (0:5/3) U (5/3:+oo)

(6*x^3-(10*x^2))/(3*x^3-(2*x^2)-(5*x)) = 0

(6*x^3-10*x^2)/(3*x^3-2*x^2-5*x) = 0

6*x^3-10*x^2 = 0

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

3*x-5 = 0 // + 5

3*x = 5 // : 3

x = 5/3

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

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

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

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

DELTA = (-2)^2-(-5*3*4)

DELTA = 64

DELTA > 0

x = (64^(1/2)+2)/(2*3) or x = (2-64^(1/2))/(2*3)

x = 5/3 or x = -1

x*(x+1)*(x-5/3) = 0

(2*x^2*(x-5/3))/(x*(x+1)*(x-5/3)) = 0

( 2*x^2 )

2*x^2 = 0 // : 2

x^2 = 0

x = 0

( x-5/3 )

x-5/3 = 0 // + 5/3

x = 5/3

x in { 0}

x in { 5/3}

x belongs to the empty set

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