(7/w-4)=(-5/(2w-8))+4

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Solution for (7/w-4)=(-5/(2w-8))+4 equation:


D( w )

2*w-8 = 0

w = 0

2*w-8 = 0

2*w-8 = 0

2*w-8 = 0 // + 8

2*w = 8 // : 2

w = 8/2

w = 4

w = 0

w = 0

w in (-oo:0) U (0:4) U (4:+oo)

7/w-4 = 4-5/(2*w-8) // - 4-5/(2*w-8)

7/w-(-5/(2*w-8))-4-4 = 0

5*(2*w-8)^-1+7/w-4-4 = 0

5/(2*w-8)+7/w-4-4 = 0

(5*w)/(w*(2*w-8))+(7*(2*w-8))/(w*(2*w-8))+(-4*w*(2*w-8))/(w*(2*w-8))+(-4*w*(2*w-8))/(w*(2*w-8)) = 0

7*(2*w-8)-4*w*(2*w-8)-4*w*(2*w-8)+5*w = 0

19*w-8*w^2-8*w^2+32*w+32*w-56 = 0

51*w-8*w^2-8*w^2+32*w-56 = 0

83*w-16*w^2-56 = 0

83*w-16*w^2-56 = 0

83*w-16*w^2-56 = 0

DELTA = 83^2-(-56*(-16)*4)

DELTA = 3305

DELTA > 0

w = (3305^(1/2)-83)/(-16*2) or w = (-3305^(1/2)-83)/(-16*2)

w = (3305^(1/2)-83)/(-32) or w = (3305^(1/2)+83)/32

(w-((3305^(1/2)-83)/(-32)))*(w-((3305^(1/2)+83)/32)) = 0

((w-((3305^(1/2)-83)/(-32)))*(w-((3305^(1/2)+83)/32)))/(w*(2*w-8)) = 0

((w-((3305^(1/2)-83)/(-32)))*(w-((3305^(1/2)+83)/32)))/(w*(2*w-8)) = 0 // * w*(2*w-8)

(w-((3305^(1/2)-83)/(-32)))*(w-((3305^(1/2)+83)/32)) = 0

( w-((3305^(1/2)+83)/32) )

w-((3305^(1/2)+83)/32) = 0 // + (3305^(1/2)+83)/32

w = (3305^(1/2)+83)/32

( w-((3305^(1/2)-83)/(-32)) )

w-((3305^(1/2)-83)/(-32)) = 0 // + (3305^(1/2)-83)/(-32)

w = (3305^(1/2)-83)/(-32)

w in { (3305^(1/2)+83)/32, (3305^(1/2)-83)/(-32) }

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