6w^4*x^2-8u^2*x/4x^3

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Solution for 6w^4*x^2-8u^2*x/4x^3 equation: 


x in (-oo:+oo)

6*w^4*x^2-(((8*u^2*x)/4)*x^3) = 0

6*w^4*x^2-2*u^2*x^4 = 0

t_1 = x^2

6*t_1^1*w^4-2*t_1^2*u^2 = 0

6*t_1*w^4-2*t_1^2*u^2 = 0

DELTA = (6*w^4)^2-(-2*0*4*u^2)

DELTA = 36*w^8

36*w^8 = 0

36*w^8 = 0 // : 36

w^8 = 0

w = 0

DELTA = 0  <=>  t_2 = 0

t_1 = (-(6*w^4))/(-2*2*u^2) i w = 0

t_1 = (3/2)*u^-2*w^4 i w = 0

( t_1 = ((36*w^8)^(1/2)-(6*w^4))/(-2*2*u^2) or t_1 = (-(6*w^4)-(36*w^8)^(1/2))/(-2*2*u^2) ) i w > 0

( t_1 = 0 or t_1 = 3*u^-2*w^4 ) i w > 0

w+0 > 0

w > 0

w+0 > 0 // - 0

w > 0

t_1 = (3/2)*u^-2*w^4

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

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

1*x^2 = -(-3/2*u^-2*w^4) // : 1

x^2 = 3/2*u^-2*w^4

x^2 = 3/2*u^-2*w^4 // ^ 1/2

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

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

t_1 = 0

x^2+0 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

t_1 = 3*u^-2*w^4

x^2-(3*u^-2*w^4) = 0

x^2-3*u^-2*w^4 = 0

1*x^2 = -(-3*u^-2*w^4) // : 1

x^2 = 3*u^-2*w^4

x^2 = 3*u^-2*w^4 // ^ 1/2

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

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

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

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