5/x+2+3/2(x+2)=1/x+2+22

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Solution for 5/x+2+3/2(x+2)=1/x+2+22 equation: 


D( x )

x = 0

x = 0

x = 0

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

(3/2)*(x+2)+5/x+2 = 1/x+2+22 // - 1/x+2+22

(3/2)*(x+2)+5/x-(1/x)-22-2+2 = 0

(3/2)*(x+2)+5/x-x^-1-22-2+2 = 0

3/2*(x+2)+5/x-1/x-22-2+2 = 0

(3/2*x*(x+2))/x+5/x-1/x+(-22*x)/x+(-2*x)/x+(2*x)/x = 0

3/2*x*(x+2)-22*x-2*x+2*x-1+5 = 0

3/2*x^2+3*x-22*x-2*x+2*x-1+5 = 0

3/2*x^2+3*x-22*x-2*x+2*x+4 = 0

3/2*x^2-19*x-2*x+2*x+4 = 0

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

3/2*x^2-19*x+4 = 0

3/2*x^2-19*x+4 = 0

3/2*x^2-19*x+4 = 0

DELTA = (-19)^2-(3/2*4*4)

DELTA = 337

DELTA > 0

x = (337^(1/2)+19)/(3/2*2) or x = (19-337^(1/2))/(3/2*2)

x = (337^(1/2)+19)/3 or x = (19-337^(1/2))/3

(x-((19-337^(1/2))/3))*(x-((337^(1/2)+19)/3)) = 0

((x-((19-337^(1/2))/3))*(x-((337^(1/2)+19)/3)))/x = 0

((x-((19-337^(1/2))/3))*(x-((337^(1/2)+19)/3)))/x = 0 // * x

(x-((19-337^(1/2))/3))*(x-((337^(1/2)+19)/3)) = 0

( x-((19-337^(1/2))/3) )

x-((19-337^(1/2))/3) = 0 // + (19-337^(1/2))/3

x = (19-337^(1/2))/3

( x-((337^(1/2)+19)/3) )

x-((337^(1/2)+19)/3) = 0 // + (337^(1/2)+19)/3

x = (337^(1/2)+19)/3

x in { (19-337^(1/2))/3, (337^(1/2)+19)/3 }

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