(3/4x)-(3/16)=(3/x)

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Solution for (3/4x)-(3/16)=(3/x) equation: 


D( x )

x = 0

x = 0

x = 0

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

(3/4)*x-(3/16) = 3/x // - 3/x

(3/4)*x-(3/x)-(3/16) = 0

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

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

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

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

x^1

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

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

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

DELTA = 2313/256

DELTA > 0

x = ((2313/256)^(1/2)-(-3/16))/(2*(3/4)) or x = (-(-3/16)-(2313/256)^(1/2))/(2*(3/4))

x = 2/3*((2313/256)^(1/2)+3/16) or x = 2/3*(3/16-(2313/256)^(1/2))

x in { 2/3*(3/16-(2313/256)^(1/2)), 2/3*((2313/256)^(1/2)+3/16)} 

x in { 2/3*(3/16-(2313/256)^(1/2)), 2/3*((2313/256)^(1/2)+3/16) }

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