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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
3*x^2-(10*x)+7/x+4 = 0
3*x^2-10*x+7/x+4 = 0
3*x^2-10*x^1+7*x^-1+4*x^0 = 0
(3*x^3-10*x^2+4*x^1+7*x^0)/(x^1) = 0 // * x^2
x^1*(3*x^3-10*x^2+4*x^1+7*x^0) = 0
x^1
3*x^3-10*x^2+4*x+7 = 0
{ 1, -1, 7, -7 }
1
x = 1
3*x^3-10*x^2+4*x+7 = 4
1
-1
x = -1
3*x^3-10*x^2+4*x+7 = -10
-1
7
x = 7
3*x^3-10*x^2+4*x+7 = 574
7
-7
x = -7
3*x^3-10*x^2+4*x+7 = -1540
-7
{ 1/3, -1/3, -1/3, 1/3, 7/3, -7/3, -7/3, 7/3 }
1/3
x
1/3
3*x^3-10*x^2+4*x+7 = 7.33333333
1/3
-1/3
x
-1/3
3*x^3-10*x^2+4*x+7 = 4.44444445
-1/3
-1/3
x
-1/3
3*x^3-10*x^2+4*x+7 = 4.44444445
-1/3
1/3
x
1/3
3*x^3-10*x^2+4*x+7 = 7.33333333
1/3
7/3
x
7/3
3*x^3-10*x^2+4*x+7 = 0
7/3
x-7/3
3*x^2-3*x-3
3*x^3-10*x^2+4*x+7
x-7/3
7*x^2-3*x^3
4*x-3*x^2+7
3*x^2-7*x
7-3*x
3*x-7
0
3*x^2-3*x-3 = 0
DELTA = (-3)^2-(-3*3*4)
DELTA = 45
DELTA > 0
x = (45^(1/2)+3)/(2*3) or x = (3-45^(1/2))/(2*3)
x = (3*5^(1/2)+3)/6 or x = (3-3*5^(1/2))/6
x in { (3-3*5^(1/2))/6, (3*5^(1/2)+3)/6, 7/3}
x in { (3-3*5^(1/2))/6, (3*5^(1/2)+3)/6, 7/3 }
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