(1/x+4)+(2/x+3)=(-1/(x*x)+7x+12)

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Solution for (1/x+4)+(2/x+3)=(-1/(x*x)+7x+12) equation: 


D( x )

x = 0

x*x = 0

x = 0

x = 0

x*x = 0

x*x = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

1/x+2/x+3+4 = 7*x-1/(x*x)+12 // - 7*x-1/(x*x)+12

1/x-(7*x)+2/x-(-1/(x*x))-12+3+4 = 0

1/x-7*x+2/x+x^-2-12+3+4 = 0

3*x^-1-7*x^1+1*x^-2-5*x^0 = 0

(3*x^1-7*x^3-5*x^2+1*x^0)/(x^2) = 0 // * x^4

x^2*(3*x^1-7*x^3-5*x^2+1*x^0) = 0

x^2

3*x-7*x^3-5*x^2+1 = 0

{ 1, -1 }

1

x = 1

3*x-7*x^3-5*x^2+1 = -8

1

-1

x = -1

3*x-7*x^3-5*x^2+1 = 0

-1

x+1

2*x-7*x^2+1

3*x-7*x^3-5*x^2+1

x+1

7*x^3+7*x^2

2*x^2+3*x+1

-2*x^2-2*x

x+1

-x-1

0

2*x-7*x^2+1 = 0

DELTA = 2^2-(-7*1*4)

DELTA = 32

DELTA > 0

x = (32^(1/2)-2)/(-7*2) or x = (-32^(1/2)-2)/(-7*2)

x = (4*2^(1/2)-2)/(-14) or x = (-4*2^(1/2)-2)/(-14)

x in { (4*2^(1/2)-2)/(-14), (-4*2^(1/2)-2)/(-14), -1} 

x in { (4*2^(1/2)-2)/(-14), (-4*2^(1/2)-2)/(-14), -1 }

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