(2/x)+2=(5/3x)+(19/9)

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Solution for (2/x)+2=(5/3x)+(19/9) equation:


D( x )

x = 0

x = 0

x = 0

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

2/x+2 = (5/3)*x+19/9 // - (5/3)*x+19/9

2/x-((5/3)*x)-(19/9)+2 = 0

(-5/3)*x+2/x-19/9+2 = 0

2*x^-1-5/3*x^1-1/9*x^0 = 0

(2*x^0-5/3*x^2-1/9*x^1)/(x^1) = 0 // * x^2

x^1*(2*x^0-5/3*x^2-1/9*x^1) = 0

x^1

(-5/3)*x^2+(-1/9)*x+2 = 0

(-5/3)*x^2+(-1/9)*x+2 = 0

DELTA = (-1/9)^2-(2*4*(-5/3))

DELTA = 1081/81

DELTA > 0

x = ((1081/81)^(1/2)-(-1/9))/(2*(-5/3)) or x = (-(-1/9)-(1081/81)^(1/2))/(2*(-5/3))

x = -3/10*((1081/81)^(1/2)+1/9) or x = -3/10*(1/9-(1081/81)^(1/2))

x in { -3/10*((1081/81)^(1/2)+1/9), -3/10*(1/9-(1081/81)^(1/2))}

x in { -3/10*((1081/81)^(1/2)+1/9), -3/10*(1/9-(1081/81)^(1/2)) }

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