(3x^4-12x^2-16)/x^2

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Solution for (3x^4-12x^2-16)/x^2 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

(3*x^4-(12*x^2)-16)/(x^2) = 0

(3*x^4-12*x^2-16)/(x^2) = 0

(3*x^4-(12*x^2)-16)/(x^2) = 0 // * x^2

3*x^4-(12*x^2)-16 = 0

3*x^4-12*x^2-16 = 0

t_1 = x^2

3*t_1^2-12*t_1^1-16 = 0

3*t_1^2-12*t_1-16 = 0

DELTA = (-12)^2-(-16*3*4)

DELTA = 336

DELTA > 0

t_1 = (336^(1/2)+12)/(2*3) or t_1 = (12-336^(1/2))/(2*3)

t_1 = (4*21^(1/2)+12)/6 or t_1 = (12-4*21^(1/2))/6

t_1 = (12-4*21^(1/2))/6

x^2-((12-4*21^(1/2))/6) = 0

1*x^2 = (12-4*21^(1/2))/6 // : 1

x^2 = (12-4*21^(1/2))/6

t_1 = (4*21^(1/2)+12)/6

x^2-((4*21^(1/2)+12)/6) = 0

1*x^2 = (4*21^(1/2)+12)/6 // : 1

x^2 = (4*21^(1/2)+12)/6

x^2 = (4*21^(1/2)+12)/6 // ^ 1/2

abs(x) = ((4*21^(1/2)+12)^(1/2))/(6^(1/2))

x = ((4*21^(1/2)+12)^(1/2))/(6^(1/2)) or x = -(((4*21^(1/2)+12)^(1/2))/(6^(1/2)))

x in { ((4*21^(1/2)+12)^(1/2))/(6^(1/2)), -(((4*21^(1/2)+12)^(1/2))/(6^(1/2))) }

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