6/4x-5/16=4/x

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Solution for 6/4x-5/16=4/x equation:


D( x )

x = 0

x = 0

x = 0

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

(6/4)*x-(5/16) = 4/x // - 4/x

(6/4)*x-(4/x)-(5/16) = 0

(6/4)*x-4*x^-1-5/16 = 0

3/2*x^1-4*x^-1-5/16*x^0 = 0

(3/2*x^2-5/16*x^1-4*x^0)/(x^1) = 0 // * x^2

x^1*(3/2*x^2-5/16*x^1-4*x^0) = 0

x^1

(3/2)*x^2+(-5/16)*x-4 = 0

(3/2)*x^2+(-5/16)*x-4 = 0

DELTA = (-5/16)^2-(-4*4*(3/2))

DELTA = 6169/256

DELTA > 0

x = ((6169/256)^(1/2)-(-5/16))/(2*(3/2)) or x = (-(-5/16)-(6169/256)^(1/2))/(2*(3/2))

x = ((6169/256)^(1/2)+5/16)/3 or x = (5/16-(6169/256)^(1/2))/3

x in { (5/16-(6169/256)^(1/2))/3, ((6169/256)^(1/2)+5/16)/3}

x in { (5/16-(6169/256)^(1/2))/3, ((6169/256)^(1/2)+5/16)/3 }

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