4x-7/x-2=3-1/2-x

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Solution for 4x-7/x-2=3-1/2-x equation: 


D( x )

x = 0

x = 0

x = 0

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

4*x-(7/x)-2 = 3-x-(1/2) // - 3-x-(1/2)

4*x+x-(7/x)+1/2-3-2 = 0

4*x+x-7*x^-1+1/2-3-2 = 0

5*x^1-7*x^-1-9/2*x^0 = 0

(5*x^2-9/2*x^1-7*x^0)/(x^1) = 0 // * x^2

x^1*(5*x^2-9/2*x^1-7*x^0) = 0

x^1

5*x^2+(-9/2)*x-7 = 0

5*x^2+(-9/2)*x-7 = 0

DELTA = (-9/2)^2-(-7*4*5)

DELTA = 641/4

DELTA > 0

x = ((641/4)^(1/2)-(-9/2))/(2*5) or x = (-(-9/2)-(641/4)^(1/2))/(2*5)

x = ((641/4)^(1/2)+9/2)/10 or x = (9/2-(641/4)^(1/2))/10

x in { (9/2-(641/4)^(1/2))/10, ((641/4)^(1/2)+9/2)/10} 

x in { (9/2-(641/4)^(1/2))/10, ((641/4)^(1/2)+9/2)/10 }

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