(3/2x+1)-(10/x-3)=1

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Solution for (3/2x+1)-(10/x-3)=1 equation:


D( x )

x = 0

x = 0

x = 0

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

(3/2)*x-(10/x)+1+3 = 1 // - 1

(3/2)*x-(10/x)-1+1+3 = 0

(3/2)*x-10*x^-1-1+1+3 = 0

3/2*x^1-10*x^-1+3*x^0 = 0

(3/2*x^2+3*x^1-10*x^0)/(x^1) = 0 // * x^2

x^1*(3/2*x^2+3*x^1-10*x^0) = 0

x^1

(3/2)*x^2+3*x-10 = 0

(3/2)*x^2+3*x-10 = 0

DELTA = 3^2-(-10*4*(3/2))

DELTA = 69

DELTA > 0

x = (69^(1/2)-3)/(2*(3/2)) or x = (-69^(1/2)-3)/(2*(3/2))

x = (69^(1/2)-3)/3 or x = (-(69^(1/2)+3))/3

x in { (-(69^(1/2)+3))/3, (69^(1/2)-3)/3}

x in { (-(69^(1/2)+3))/3, (69^(1/2)-3)/3 }

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