(6x^4+6x^3-x^2)/(3x^2+1)

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Solution for (6x^4+6x^3-x^2)/(3x^2+1) equation:


D( x )

3*x^2+1 = 0

3*x^2+1 = 0

3*x^2+1 = 0

3*x^2 = -1 // : 3

x^2 = -1/3

x in (-oo:+oo)

(6*x^4+6*x^3-x^2)/(3*x^2+1) = 0

6*x^4+6*x^3-x^2 = 0

x^2*(6*x^2+6*x-1) = 0

6*x^2+6*x-1 = 0

DELTA = 6^2-(-1*4*6)

DELTA = 60

DELTA > 0

x = (60^(1/2)-6)/(2*6) or x = (-60^(1/2)-6)/(2*6)

x = (2*15^(1/2)-6)/12 or x = (-2*15^(1/2)-6)/12

x^2*(x-((-2*15^(1/2)-6)/12))*(x-((2*15^(1/2)-6)/12)) = 0

(x^2*(x-((-2*15^(1/2)-6)/12))*(x-((2*15^(1/2)-6)/12)))/(3*x^2+1) = 0

( x-((-2*15^(1/2)-6)/12) )

x-((-2*15^(1/2)-6)/12) = 0 // + (-2*15^(1/2)-6)/12

x = (-2*15^(1/2)-6)/12

( x-((2*15^(1/2)-6)/12) )

x-((2*15^(1/2)-6)/12) = 0 // + (2*15^(1/2)-6)/12

x = (2*15^(1/2)-6)/12

( x^2 )

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in { (-2*15^(1/2)-6)/12, (2*15^(1/2)-6)/12, 0 }

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