8/x+9=5/2x+15/4

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Solution for 8/x+9=5/2x+15/4 equation: 


D( x )

x = 0

x = 0

x = 0

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

8/x+9 = (5/2)*x+15/4 // - (5/2)*x+15/4

8/x-((5/2)*x)-(15/4)+9 = 0

(-5/2)*x+8/x-15/4+9 = 0

8*x^-1-5/2*x^1+21/4*x^0 = 0

(21/4*x^1-5/2*x^2+8*x^0)/(x^1) = 0 // * x^2

x^1*(21/4*x^1-5/2*x^2+8*x^0) = 0

x^1

(-5/2)*x^2+(21/4)*x+8 = 0

(-5/2)*x^2+(21/4)*x+8 = 0

DELTA = (21/4)^2-(4*8*(-5/2))

DELTA = 1721/16

DELTA > 0

x = ((1721/16)^(1/2)-(21/4))/(2*(-5/2)) or x = (-(21/4)-(1721/16)^(1/2))/(2*(-5/2))

x = ((1721/16)^(1/2)-21/4)/(-5) or x = ((1721/16)^(1/2)+21/4)/5

x in { ((1721/16)^(1/2)-21/4)/(-5), ((1721/16)^(1/2)+21/4)/5} 

x in { ((1721/16)^(1/2)-21/4)/(-5), ((1721/16)^(1/2)+21/4)/5 }

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