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

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

4*(2*x-1)-3*x*x = 0

8*x-3*x^2-4 = 0

8*x-3*x^2-4 = 0

8*x-3*x^2-4 = 0

DELTA = 8^2-(-4*(-3)*4)

DELTA = 16

DELTA > 0

x = (16^(1/2)-8)/(-3*2) or x = (-16^(1/2)-8)/(-3*2)

x = 2/3 or x = 2

(x-2/3)*(x-2) = 0

((x-2/3)*(x-2))/(4*x) = 0

((x-2/3)*(x-2))/(4*x) = 0 // * 4*x

(x-2/3)*(x-2) = 0

( x-2/3 )

x-2/3 = 0 // + 2/3

x = 2/3

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 2/3, 2 }

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