((8x^3)/((x^2+49)^3))-(6x/((x^2+49)^2))=0

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Solution for ((8x^3)/((x^2+49)^3))-(6x/((x^2+49)^2))=0 equation: 


D( x )

(x^2+49)^3 = 0

(x^2+49)^2 = 0

(x^2+49)^3 = 0

(x^2+49)^3 = 0

1*x^2 = -49 // : 1

x^2 = -49

(x^2+49)^2 = 0

(x^2+49)^2 = 0

1*x^2 = -49 // : 1

x^2 = -49

x in (-oo:+oo)

(8*x^3)/((x^2+49)^3)-((6*x)/((x^2+49)^2)) = 0

(8*x^3)/((x^2+49)^3)-6*x*(x^2+49)^-2 = 0

(8*x^3)/((x^2+49)^3)+(-6*x)/((x^2+49)^2) = 0

(8*x^3)/((x^2+49)^3)+(-6*x*(x^2+49))/((x^2+49)^3) = 0

8*x^3-6*x*(x^2+49) = 0

2*x^3-294*x = 0

2*x^3-294*x = 0

2*x*(x^2-147) = 0

1*x^2 = 147 // : 1

x^2 = 147

x^2 = 147 // ^ 1/2

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

x = 7*3^(1/2) or x = -(7*3^(1/2))

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

(2*x*(x-7*3^(1/2))*(x+7*3^(1/2)))/((x^2+49)^3) = 0

(2*x*(x-7*3^(1/2))*(x+7*3^(1/2)))/((x^2+49)^3) = 0 // * (x^2+49)^3

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

( 2*x )

2*x = 0 // : 2

x = 0

( x+7*3^(1/2) )

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

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

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

( x-7*3^(1/2) )

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

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

x = 7*3^(1/2)

x in { 0, -7*3^(1/2), 7*3^(1/2) }

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