(5x^3-4x)/(7x^3-2)

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Solution for (5x^3-4x)/(7x^3-2) equation: 


D( x )

7*x^3-2 = 0

7*x^3-2 = 0

7*x^3-2 = 0

7*x^3 = 2 // : 7

x^3 = 2/7

x^3 = 2/7 // ^ 1/3

x = (2/7)^(1/3)

x in (-oo:(2/7)^(1/3)) U ((2/7)^(1/3):+oo)

(5*x^3-(4*x))/(7*x^3-2) = 0

(5*x^3-4*x)/(7*x^3-2) = 0

5*x^3-4*x = 0

x*(5*x^2-4) = 0

5*x^2 = 4 // : 5

x^2 = 4/5

x^2 = 4/5 // ^ 1/2

abs(x) = (4/5)^(1/2)

x = (4/5)^(1/2) or x = -(4/5)^(1/2)

x*(x-(4/5)^(1/2))*(x+(4/5)^(1/2)) = 0

(x*(x-(4/5)^(1/2))*(x+(4/5)^(1/2)))/(7*x^3-2) = 0

( x+(4/5)^(1/2) )

x+(4/5)^(1/2) = 0 // - (4/5)^(1/2)

x = -(4/5)^(1/2)

( x-(4/5)^(1/2) )

x-(4/5)^(1/2) = 0 // + (4/5)^(1/2)

x = (4/5)^(1/2)

( x )

x = 0

x in { -(4/5)^(1/2), (4/5)^(1/2), 0 }

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