2/3x-5=4/x-15

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Solution for 2/3x-5=4/x-15 equation: 


D( x )

x = 0

x = 0

x = 0

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

(2/3)*x-5 = 4/x-15 // - 4/x-15

(2/3)*x-(4/x)-5+15 = 0

(2/3)*x-4*x^-1-5+15 = 0

2/3*x^1-4*x^-1+10*x^0 = 0

(2/3*x^2+10*x^1-4*x^0)/(x^1) = 0 // * x^2

x^1*(2/3*x^2+10*x^1-4*x^0) = 0

x^1

(2/3)*x^2+10*x-4 = 0

(2/3)*x^2+10*x-4 = 0

DELTA = 10^2-(-4*4*(2/3))

DELTA = 332/3

DELTA > 0

x = ((332/3)^(1/2)-10)/(2*(2/3)) or x = (-(332/3)^(1/2)-10)/(2*(2/3))

x = 3/4*((332/3)^(1/2)-10) or x = -3/4*((332/3)^(1/2)+10)

x in { -3/4*((332/3)^(1/2)+10), 3/4*((332/3)^(1/2)-10)} 

x in { -3/4*((332/3)^(1/2)+10), 3/4*((332/3)^(1/2)-10) }

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