3/x=x-10/8

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Solution for 3/x=x-10/8 equation: 


D( x )

x = 0

x = 0

x = 0

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

3/x = x-(10/8) // - x-(10/8)

3/x-x+10/8 = 0

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

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

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

x^1

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

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

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

DELTA = 217/16

DELTA > 0

x = ((217/16)^(1/2)-(5/4))/(-1*2) or x = (-(5/4)-(217/16)^(1/2))/(-1*2)

x = ((217/16)^(1/2)-5/4)/(-2) or x = ((217/16)^(1/2)+5/4)/2

x in { ((217/16)^(1/2)-5/4)/(-2), ((217/16)^(1/2)+5/4)/2} 

x in { ((217/16)^(1/2)-5/4)/(-2), ((217/16)^(1/2)+5/4)/2 }

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