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D( x )
2*x-9 = 0
2*x-9 = 0
2*x-9 = 0
2*x-9 = 0 // + 9
2*x = 9 // : 2
x = 9/2
x in (-oo:9/2) U (9/2:+oo)
3/(2*x-9) = 8-(3*x) // - 8-(3*x)
3/(2*x-9)+3*x-8 = 0
3/(2*x-9)+(3*x*(2*x-9))/(2*x-9)+(-8*(2*x-9))/(2*x-9) = 0
3*x*(2*x-9)-8*(2*x-9)+3 = 0
6*x^2-27*x-16*x+3+72 = 0
6*x^2-43*x+75 = 0
6*x^2-43*x+75 = 0
6*x^2-43*x+75 = 0
DELTA = (-43)^2-(4*6*75)
DELTA = 49
DELTA > 0
x = (49^(1/2)+43)/(2*6) or x = (43-49^(1/2))/(2*6)
x = 25/6 or x = 3
(x-3)*(x-25/6) = 0
((x-3)*(x-25/6))/(2*x-9) = 0
((x-3)*(x-25/6))/(2*x-9) = 0 // * 2*x-9
(x-3)*(x-25/6) = 0
( x-25/6 )
x-25/6 = 0 // + 25/6
x = 25/6
( x-3 )
x-3 = 0 // + 3
x = 3
x in { 25/6, 3 }
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