12a^3x^2-6a^2x^4/6a^3x^2

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Solution for 12a^3x^2-6a^2x^4/6a^3x^2 equation: 


x in (-oo:+oo)

12*a^3*x^2-(((6*a^2*x^4)/6)*a^3*x^2) = 0

12*a^3*x^2-(a^5*x^6) = 0

t_1 = x^2

12*a^3*t_1^1-a^5*t_1^3 = 0

12*a^3*t_1-(a^5*t_1^3) = 0

a^3*t_1*(12-(a^2*t_1^2)) = 0

-a^2*t_1^2 = -12 // : -a^2

t_1^2 = 12/(a^2)

t_1^2 = 12/(a^2) // ^ 1/2

abs(t_1) = (2*3^(1/2))/a

t_1 = (2*3^(1/2))/a or t_1 = -((2*3^(1/2))/a)

a^3*t_1 = 0

a^3*t_1 = 0 // : a^3

t_1 = 0

t_1 = (2*3^(1/2))/a

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

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

1*x^2 = -(-2*3^(1/2)*a^-1) // : 1

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

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

abs(x) = 2^(1/2)*3^(1/4)*a^(-1/2)

x = 2^(1/2)*3^(1/4)*a^(-1/2) or x = -(2^(1/2)*3^(1/4)*a^(-1/2))

t_1 = -((2*3^(1/2))/a)

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

1*x^2 = -(2*3^(1/2)*a^-1) // : 1

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

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

abs(x) = (-2*3^(1/2))^(1/2)*a^(-1/2)

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

t_1 = 0

x^2+0 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in { 2^(1/2)*3^(1/4)*a^(-1/2), -(2^(1/2)*3^(1/4)*a^(-1/2)), (-2*3^(1/2))^(1/2)*a^(-1/2), -((-2*3^(1/2))^(1/2)*a^(-1/2)), 0 }

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