2/x+4=8/3x+37/9

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Solution for 2/x+4=8/3x+37/9 equation: 


D( x )

x = 0

x = 0

x = 0

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

2/x+4 = (8/3)*x+37/9 // - (8/3)*x+37/9

2/x-((8/3)*x)-(37/9)+4 = 0

(-8/3)*x+2/x-37/9+4 = 0

2*x^-1-8/3*x^1-1/9*x^0 = 0

(2*x^0-8/3*x^2-1/9*x^1)/(x^1) = 0 // * x^2

x^1*(2*x^0-8/3*x^2-1/9*x^1) = 0

x^1

(-8/3)*x^2+(-1/9)*x+2 = 0

(-8/3)*x^2+(-1/9)*x+2 = 0

DELTA = (-1/9)^2-(2*4*(-8/3))

DELTA = 1729/81

DELTA > 0

x = ((1729/81)^(1/2)-(-1/9))/(2*(-8/3)) or x = (-(-1/9)-(1729/81)^(1/2))/(2*(-8/3))

x = -3/16*((1729/81)^(1/2)+1/9) or x = -3/16*(1/9-(1729/81)^(1/2))

x in { -3/16*((1729/81)^(1/2)+1/9), -3/16*(1/9-(1729/81)^(1/2))} 

x in { -3/16*((1729/81)^(1/2)+1/9), -3/16*(1/9-(1729/81)^(1/2)) }

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