(2/x)-4/3x=8+3/x

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Solution for (2/x)-4/3x=8+3/x equation: 


D( x )

x = 0

x = 0

x = 0

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

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

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

(-4/3)*x+2/x-3*x^-1-8 = 0

-4/3*x^1-1*x^-1-8*x^0 = 0

(-4/3*x^2-8*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(-4/3*x^2-8*x^1-1*x^0) = 0

x^1

(-4/3)*x^2-8*x-1 = 0

(-4/3)*x^2-8*x-1 = 0

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

DELTA = 176/3

DELTA > 0

x = ((176/3)^(1/2)+8)/(2*(-4/3)) or x = (8-(176/3)^(1/2))/(2*(-4/3))

x = -3/8*((176/3)^(1/2)+8) or x = -3/8*(8-(176/3)^(1/2))

x in { -3/8*((176/3)^(1/2)+8), -3/8*(8-(176/3)^(1/2))} 

x in { -3/8*((176/3)^(1/2)+8), -3/8*(8-(176/3)^(1/2)) }

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