7/1+13/w=12/w^2

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Solution for 7/1+13/w=12/w^2 equation: 


D( w )

w^2 = 0

w = 0

w^2 = 0

w^2 = 0

1*w^2 = 0 // : 1

w^2 = 0

w = 0

w = 0

w = 0

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

13/w+7/1 = 12/(w^2) // - 12/(w^2)

13/w-(12/(w^2))+7/1 = 0

13/w-12*w^-2+7 = 0

13*w^-1-12*w^-2+7 = 0

t_1 = w^-1

13*t_1^1-12*t_1^2+7 = 0

13*t_1-12*t_1^2+7 = 0

DELTA = 13^2-(-12*4*7)

DELTA = 505

DELTA > 0

t_1 = (505^(1/2)-13)/(-12*2) or t_1 = (-505^(1/2)-13)/(-12*2)

t_1 = (505^(1/2)-13)/(-24) or t_1 = (505^(1/2)+13)/24

t_1 = (505^(1/2)-13)/(-24)

w^-1-((505^(1/2)-13)/(-24)) = 0

1*w^-1 = (505^(1/2)-13)/(-24) // : 1

w^-1 = (505^(1/2)-13)/(-24)

-1 < 0

1/(w^1) = (505^(1/2)-13)/(-24) // * w^1

1 = ((505^(1/2)-13)/(-24))*w^1 // : (505^(1/2)-13)/(-24)

-24*(505^(1/2)-13)^-1 = w^1

w = -24*(505^(1/2)-13)^-1

t_1 = (505^(1/2)+13)/24

w^-1-((505^(1/2)+13)/24) = 0

1*w^-1 = (505^(1/2)+13)/24 // : 1

w^-1 = (505^(1/2)+13)/24

-1 < 0

1/(w^1) = (505^(1/2)+13)/24 // * w^1

1 = ((505^(1/2)+13)/24)*w^1 // : (505^(1/2)+13)/24

24*(505^(1/2)+13)^-1 = w^1

w = 24*(505^(1/2)+13)^-1

w in { -24*(505^(1/2)-13)^-1, 24*(505^(1/2)+13)^-1 }

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