(10x^6+8x^4)/(2x^2)=14x^4

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Solution for (10x^6+8x^4)/(2x^2)=14x^4 equation:


D( x )

2*x^2 = 0

2*x^2 = 0

2*x^2 = 0

2*x^2 = 0 // : 2

x^2 = 0

x = 0

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

(10*x^6+8*x^4)/(2*x^2) = 14*x^4 // - 14*x^4

(10*x^6+8*x^4)/(2*x^2)-(14*x^4) = 0

(10*x^6+8*x^4)/(2*x^2)-14*x^4 = 0

(10*x^6+8*x^4)/(2*x^2)+(-14*2*x^2*x^4)/(2*x^2) = 0

10*x^6-14*2*x^2*x^4+8*x^4 = 0

8*x^4-18*x^6 = 0

8*x^4-18*x^6 = 0

2*x^4*(4-9*x^2) = 0

-9*x^2 = -4 // : -9

x^2 = 4/9

x^2 = 4/9 // ^ 1/2

abs(x) = 2/3

x = 2/3 or x = -2/3

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

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

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

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

( 2*x^4 )

2*x^4 = 0 // : 2

x^4 = 0

x = 0

( x+2/3 )

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

x = -2/3

( x-2/3 )

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

x = 2/3

x in { 0}

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

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