5/2x-7/8=6/x

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Solution for 5/2x-7/8=6/x equation: 


D( x )

x = 0

x = 0

x = 0

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

(5/2)*x-(7/8) = 6/x // - 6/x

(5/2)*x-(6/x)-(7/8) = 0

(5/2)*x-6*x^-1-7/8 = 0

5/2*x^1-6*x^-1-7/8*x^0 = 0

(5/2*x^2-7/8*x^1-6*x^0)/(x^1) = 0 // * x^2

x^1*(5/2*x^2-7/8*x^1-6*x^0) = 0

x^1

(5/2)*x^2+(-7/8)*x-6 = 0

(5/2)*x^2+(-7/8)*x-6 = 0

DELTA = (-7/8)^2-(-6*4*(5/2))

DELTA = 3889/64

DELTA > 0

x = ((3889/64)^(1/2)-(-7/8))/(2*(5/2)) or x = (-(-7/8)-(3889/64)^(1/2))/(2*(5/2))

x = ((3889/64)^(1/2)+7/8)/5 or x = (7/8-(3889/64)^(1/2))/5

x in { (7/8-(3889/64)^(1/2))/5, ((3889/64)^(1/2)+7/8)/5} 

x in { (7/8-(3889/64)^(1/2))/5, ((3889/64)^(1/2)+7/8)/5 }

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