5/7x-6=2/x-3

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Solution for 5/7x-6=2/x-3 equation: 


D( x )

x = 0

x = 0

x = 0

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

(5/7)*x-6 = 2/x-3 // - 2/x-3

(5/7)*x-(2/x)-6+3 = 0

(5/7)*x-2*x^-1-6+3 = 0

5/7*x^1-2*x^-1-3*x^0 = 0

(5/7*x^2-3*x^1-2*x^0)/(x^1) = 0 // * x^2

x^1*(5/7*x^2-3*x^1-2*x^0) = 0

x^1

(5/7)*x^2-3*x-2 = 0

(5/7)*x^2-3*x-2 = 0

DELTA = (-3)^2-(-2*4*(5/7))

DELTA = 103/7

DELTA > 0

x = ((103/7)^(1/2)+3)/(2*(5/7)) or x = (3-(103/7)^(1/2))/(2*(5/7))

x = 7/10*((103/7)^(1/2)+3) or x = 7/10*(3-(103/7)^(1/2))

x in { 7/10*(3-(103/7)^(1/2)), 7/10*((103/7)^(1/2)+3)} 

x in { 7/10*(3-(103/7)^(1/2)), 7/10*((103/7)^(1/2)+3) }

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