(3+w)/(6(w))=(1/2(w))+(4/3)

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Solution for (3+w)/(6(w))=(1/2(w))+(4/3) equation: 


D( w )

6*w = 0

6*w = 0

6*w = 0

6*w = 0 // : 6

w = 0

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

(w+3)/(6*w) = (1/2)*w+4/3 // - (1/2)*w+4/3

(w+3)/(6*w)-((1/2)*w)-(4/3) = 0

(w+3)/(6*w)+(-1/2)*w-4/3 = 0

(w+3)/(6*w)-w/2-4/3 = 0

(2*3*(w+3))/(2*3*6*w)+(3*6*(-w)*w)/(2*3*6*w)+(-4*2*6*w)/(2*3*6*w) = 0

2*3*(w+3)+3*6*(-w)*w-4*2*6*w = 0

6*w-18*w^2-48*w+18 = 0

18-18*w^2-42*w = 0

18-18*w^2-42*w = 0

6*(3-3*w^2-7*w) = 0

3-3*w^2-7*w = 0

DELTA = (-7)^2-(-3*3*4)

DELTA = 85

DELTA > 0

w = (85^(1/2)+7)/(-3*2) or w = (7-85^(1/2))/(-3*2)

w = (85^(1/2)+7)/(-6) or w = (7-85^(1/2))/(-6)

6*(w-((85^(1/2)+7)/(-6)))*(w-((7-85^(1/2))/(-6))) = 0

(6*(w-((85^(1/2)+7)/(-6)))*(w-((7-85^(1/2))/(-6))))/(2*3*6*w) = 0

(6*(w-((85^(1/2)+7)/(-6)))*(w-((7-85^(1/2))/(-6))))/(2*3*6*w) = 0 // * 2*3*6*w

6*(w-((85^(1/2)+7)/(-6)))*(w-((7-85^(1/2))/(-6))) = 0

( w-((7-85^(1/2))/(-6)) )

w-((7-85^(1/2))/(-6)) = 0 // + (7-85^(1/2))/(-6)

w = (7-85^(1/2))/(-6)

( w-((85^(1/2)+7)/(-6)) )

w-((85^(1/2)+7)/(-6)) = 0 // + (85^(1/2)+7)/(-6)

w = (85^(1/2)+7)/(-6)

w in { (7-85^(1/2))/(-6), (85^(1/2)+7)/(-6) }

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