3-2w/5-2/w-3

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Solution for 3-2w/5-2/w-3 equation: 


D( w )

w = 0

w = 0

w = 0

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

3-((2*w)/5)-(2/w) < -3 // + 3

3-((2*w)/5)-(2/w)+3 < 0

(-2/5)*w-2*w^-1+3+3 < 0

6-2/5*w-2*w^-1 = 0

2*(3-1/5*w-w^-1) = 0

3*w^0-1/5*w^1-1*w^-1 = 0

(3*w^1-1/5*w^2-1*w^0)/(w^1) = 0 // * w^2

w^1*(3*w^1-1/5*w^2-1*w^0) = 0

w^1

(-1/5)*w^2+3*w-1 = 0

(-1/5)*w^2+3*w-1 = 0

DELTA = 3^2-(-1*4*(-1/5))

DELTA = 41/5

DELTA > 0

w = ((41/5)^(1/2)-3)/(2*(-1/5)) or w = (-(41/5)^(1/2)-3)/(2*(-1/5))

w = -5/2*((41/5)^(1/2)-3) or w = 5/2*((41/5)^(1/2)+3)

w in { -5/2*((41/5)^(1/2)-3), 5/2*((41/5)^(1/2)+3)} 

2 = 0

2 = 0

w belongs to the empty set

(w+5/2*((41/5)^(1/2)-3))*(w-5/2*((41/5)^(1/2)+3)) < 0

	(-oo:-5/2*((41/5)^(1/2)-3))	(-5/2*((41/5)^(1/2)-3):5/2*((41/5)^(1/2)+3))	(5/2*((41/5)^(1/2)+3):+oo)
w+5/2*((41/5)^(1/2)-3)	-	+	+
w-5/2*((41/5)^(1/2)+3)	-	-	+


w in (-5/2*((41/5)^(1/2)-3):5/2*((41/5)^(1/2)+3))

(-5/2*((41/5)^(1/2)-3):5/2*((41/5)^(1/2)+3))

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