4u/u+4=24/u^2+3u-4

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Solution for 4u/u+4=24/u^2+3u-4 equation:


D( u )

u = 0

u^2 = 0

u = 0

u = 0

u^2 = 0

u^2 = 0

1*u^2 = 0 // : 1

u^2 = 0

u = 0

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

(4*u)/u+4 = 3*u+24/(u^2)-4 // - 3*u+24/(u^2)-4

(4*u)/u-(3*u)-(24/(u^2))+4+4 = 0

(4*u)/u-3*u-24*u^-2+4+4 = 0

12*u^0-3*u^1-24*u^-2 = 0

(12*u^2-3*u^3-24*u^0)/(u^2) = 0 // * u^4

u^2*(12*u^2-3*u^3-24*u^0) = 0

u^2

12*u^2-3*u^3-24 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 24, -24 }

1

u = 1

12*u^2-3*u^3-24 = -15

1

-1

u = -1

12*u^2-3*u^3-24 = -9

-1

2

u = 2

12*u^2-3*u^3-24 = 0

2

u-2

6*u-3*u^2+12

12*u^2-3*u^3-24

u-2

3*u^3-6*u^2

6*u^2-24

12*u-6*u^2

12*u-24

24-12*u

0

6*u-3*u^2+12 = 0

DELTA = 6^2-(-3*4*12)

DELTA = 180

DELTA > 0

u = (180^(1/2)-6)/(-3*2) or u = (-180^(1/2)-6)/(-3*2)

u = (6*5^(1/2)-6)/(-6) or u = (-6*5^(1/2)-6)/(-6)

u in { (6*5^(1/2)-6)/(-6), (-6*5^(1/2)-6)/(-6), 2}

u in { (6*5^(1/2)-6)/(-6), (-6*5^(1/2)-6)/(-6), 2 }

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