5/x+2+2(x+2)=1/x+2+22

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Solution for 5/x+2+2(x+2)=1/x+2+22 equation: 


D( x )

x = 0

x = 0

x = 0

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

2*(x+2)+5/x+2 = 1/x+2+22 // - 1/x+2+22

2*(x+2)+5/x-(1/x)-22-2+2 = 0

2*(x+2)+5/x-x^-1-22-2+2 = 0

2*(x+2)+5/x-1/x-22-2+2 = 0

(2*x*(x+2))/x+5/x-1/x+(-22*x)/x+(-2*x)/x+(2*x)/x = 0

2*x*(x+2)-22*x-2*x+2*x-1+5 = 0

2*x^2+4*x-22*x-2*x+2*x-1+5 = 0

2*x^2+4*x-22*x-2*x+2*x+4 = 0

2*x^2-18*x-2*x+2*x+4 = 0

2*x^2-20*x+2*x+4 = 0

2*x^2-18*x+4 = 0

2*x^2-18*x+4 = 0

2*(x^2-9*x+2) = 0

x^2-9*x+2 = 0

DELTA = (-9)^2-(1*2*4)

DELTA = 73

DELTA > 0

x = (73^(1/2)+9)/(1*2) or x = (9-73^(1/2))/(1*2)

x = (73^(1/2)+9)/2 or x = (9-73^(1/2))/2

2*(x-((9-73^(1/2))/2))*(x-((73^(1/2)+9)/2)) = 0

(2*(x-((9-73^(1/2))/2))*(x-((73^(1/2)+9)/2)))/x = 0

(2*(x-((9-73^(1/2))/2))*(x-((73^(1/2)+9)/2)))/x = 0 // * x

2*(x-((9-73^(1/2))/2))*(x-((73^(1/2)+9)/2)) = 0

( x-((73^(1/2)+9)/2) )

x-((73^(1/2)+9)/2) = 0 // + (73^(1/2)+9)/2

x = (73^(1/2)+9)/2

( x-((9-73^(1/2))/2) )

x-((9-73^(1/2))/2) = 0 // + (9-73^(1/2))/2

x = (9-73^(1/2))/2

x in { (73^(1/2)+9)/2, (9-73^(1/2))/2 }

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