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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
(2*x+3)/2+1/x = 8*x // - 8*x
(2*x+3)/2-(8*x)+1/x = 0
(2*x+3)/2-8*x+1/x = 0
(x*(2*x+3))/(2*x)+(-8*2*x*x)/(2*x)+(1*2)/(2*x) = 0
x*(2*x+3)-8*2*x*x+1*2 = 0
3*x-14*x^2+2 = 0
3*x-14*x^2+2 = 0
3*x-14*x^2+2 = 0
DELTA = 3^2-(-14*2*4)
DELTA = 121
DELTA > 0
x = (121^(1/2)-3)/(-14*2) or x = (-121^(1/2)-3)/(-14*2)
x = -2/7 or x = 1/2
(x+2/7)*(x-1/2) = 0
((x+2/7)*(x-1/2))/(2*x) = 0
((x+2/7)*(x-1/2))/(2*x) = 0 // * 2*x
(x+2/7)*(x-1/2) = 0
( x+2/7 )
x+2/7 = 0 // - 2/7
x = -2/7
( x-1/2 )
x-1/2 = 0 // + 1/2
x = 1/2
x in { -2/7, 1/2 }
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