3x+4/2x+3=x+14/x+8

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Solution for 3x+4/2x+3=x+14/x+8 equation: 


D( x )

x = 0

x = 0

x = 0

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

3*x+(4/2)*x+3 = x+14/x+8 // - x+14/x+8

3*x+(4/2)*x-x-(14/x)-8+3 = 0

3*x+(4/2)*x-x-14*x^-1-8+3 = 0

4*x^1-14*x^-1-5*x^0 = 0

(4*x^2-5*x^1-14*x^0)/(x^1) = 0 // * x^2

x^1*(4*x^2-5*x^1-14*x^0) = 0

x^1

4*x^2-5*x-14 = 0

4*x^2-5*x-14 = 0

DELTA = (-5)^2-(-14*4*4)

DELTA = 249

DELTA > 0

x = (249^(1/2)+5)/(2*4) or x = (5-249^(1/2))/(2*4)

x = (249^(1/2)+5)/8 or x = (5-249^(1/2))/8

x in { (5-249^(1/2))/8, (249^(1/2)+5)/8} 

x in { (5-249^(1/2))/8, (249^(1/2)+5)/8 }

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