3r-4/r=8/6

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Solution for 3r-4/r=8/6 equation: 


D( r )

r = 0

r = 0

r = 0

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

3*r-(4/r) = 8/6 // - 8/6

3*r-(4/r)-(8/6) = 0

3*r-4*r^-1-4/3 = 0

3*r^1-4*r^-1-4/3*r^0 = 0

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

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

r^1

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

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

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

DELTA = 448/9

DELTA > 0

r = ((448/9)^(1/2)-(-4/3))/(2*3) or r = (-(-4/3)-(448/9)^(1/2))/(2*3)

r = ((448/9)^(1/2)+4/3)/6 or r = (4/3-(448/9)^(1/2))/6

r in { (4/3-(448/9)^(1/2))/6, ((448/9)^(1/2)+4/3)/6} 

r in { (4/3-(448/9)^(1/2))/6, ((448/9)^(1/2)+4/3)/6 }

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