x-2/3x=4/x-1/5

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Solution for x-2/3x=4/x-1/5 equation:


D( x )

x = 0

x = 0

x = 0

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

x-((2/3)*x) = 4/x-(1/5) // - 4/x-(1/5)

x-((2/3)*x)-(4/x)+1/5 = 0

x+(-2/3)*x-4*x^-1+1/5 = 0

1/3*x^1-4*x^-1+1/5*x^0 = 0

(1/3*x^2+1/5*x^1-4*x^0)/(x^1) = 0 // * x^2

x^1*(1/3*x^2+1/5*x^1-4*x^0) = 0

x^1

(1/3)*x^2+(1/5)*x-4 = 0

(1/3)*x^2+(1/5)*x-4 = 0

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

DELTA = 403/75

DELTA > 0

x = ((403/75)^(1/2)-(1/5))/(2*(1/3)) or x = (-(1/5)-(403/75)^(1/2))/(2*(1/3))

x = 3/2*((403/75)^(1/2)-1/5) or x = -3/2*((403/75)^(1/2)+1/5)

x in { -3/2*((403/75)^(1/2)+1/5), 3/2*((403/75)^(1/2)-1/5)}

x in { -3/2*((403/75)^(1/2)+1/5), 3/2*((403/75)^(1/2)-1/5) }

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