(1/x+7)+(2/x+3)=(-4/x^2+10x+21)

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Solution for (1/x+7)+(2/x+3)=(-4/x^2+10x+21) equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

1/x+2/x+3+7 = 10*x-4/(x^2)+21 // - 10*x-4/(x^2)+21

1/x-(10*x)+2/x-(-4/(x^2))-21+3+7 = 0

1/x-10*x+2/x+4*x^-2-21+3+7 = 0

3*x^-1-10*x^1+4*x^-2-11*x^0 = 0

(3*x^1-10*x^3-11*x^2+4*x^0)/(x^2) = 0 // * x^4

x^2*(3*x^1-10*x^3-11*x^2+4*x^0) = 0

x^2

3*x-10*x^3-11*x^2+4 = 0

{ 1, -1, 2, -2, 4, -4 }

1

x = 1

3*x-10*x^3-11*x^2+4 = -14

1

-1

x = -1

3*x-10*x^3-11*x^2+4 = 0

-1

x+1

4-10*x^2-x

3*x-10*x^3-11*x^2+4

x+1

10*x^3+10*x^2

3*x-x^2+4

x^2+x

4*x+4

-4*x-4

0

4-10*x^2-x = 0

DELTA = (-1)^2-(-10*4*4)

DELTA = 161

DELTA > 0

x = (161^(1/2)+1)/(-10*2) or x = (1-161^(1/2))/(-10*2)

x = (161^(1/2)+1)/(-20) or x = (1-161^(1/2))/(-20)

x in { (161^(1/2)+1)/(-20), (1-161^(1/2))/(-20), -1} 

x in { (161^(1/2)+1)/(-20), (1-161^(1/2))/(-20), -1 }

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