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D( x )
6*x-10 = 0
6*x-10 = 0
6*x-10 = 0
6*x-10 = 0 // + 10
6*x = 10 // : 6
x = 10/6
x = 5/3
x in (-oo:5/3) U (5/3:+oo)
(30*x^3+4*x^2-150)/(6*x-10) = 0
30*x^3+4*x^2-150 = 0
2*(15*x^3+2*x^2-75) = 0
15*x^3+2*x^2-75 = 0
{ 1, -1, 3, -3, 5, -5, 15, -15, 25, -25, 75, -75 }
1
x = 1
15*x^3+2*x^2-75 = -58
1
-1
x = -1
15*x^3+2*x^2-75 = -88
-1
3
x = 3
15*x^3+2*x^2-75 = 348
3
-3
x = -3
15*x^3+2*x^2-75 = -462
-3
5
x = 5
15*x^3+2*x^2-75 = 1850
5
-5
x = -5
15*x^3+2*x^2-75 = -1900
-5
15
x = 15
15*x^3+2*x^2-75 = 51000
15
-15
x = -15
15*x^3+2*x^2-75 = -50250
-15
25
x = 25
15*x^3+2*x^2-75 = 235550
25
-25
x = -25
15*x^3+2*x^2-75 = -233200
-25
75
x = 75
15*x^3+2*x^2-75 = 6339300
75
-75
x = -75
15*x^3+2*x^2-75 = -6316950
-75
{ 1/3, -1/3, 1/5, -1/5, 1/15, -1/15, -1/3, 1/3, -1/5, 1/5, -1/15, 1/15, 3/3, -3/3, 3/5, -3/5, 3/15, -3/15, -3/3, 3/3, -3/5, 3/5, -3/15, 3/15, 5/3, -5/3, 5/5, -5/5, 5/15, -5/15, -5/3, 5/3, -5/5, 5/5, -5/15, 5/15, 15/3, -15/3, 15/5, -15/5, 15/15, -15/15, -15/3, 15/3, -15/5, 15/5, -15/15, 15/15, 25/3, -25/3, 25/5, -25/5, 25/15, -25/15, -25/3, 25/3, -25/5, 25/5, -25/15, 25/15, 75/3, -75/3, 75/5, -75/5, 75/15, -75/15, -75/3, 75/3, -75/5, 75/5, -75/15, 75/15 }
1/3
x
1/3
15*x^3+2*x^2-75 = -74.22222222
1/3
-1/3
x
-1/3
15*x^3+2*x^2-75 = -75.33333334
-1/3
1/5
x
1/5
15*x^3+2*x^2-75 = -74.8
1/5
-1/5
x
-1/5
15*x^3+2*x^2-75 = -75.04
-1/5
1/15
x
1/15
15*x^3+2*x^2-75 = -74.98666667
1/15
-1/15
x
-1/15
15*x^3+2*x^2-75 = -74.99555555
-1/15
-1/3
x
-1/3
15*x^3+2*x^2-75 = -75.33333334
-1/3
1/3
x
1/3
15*x^3+2*x^2-75 = -74.22222222
1/3
-1/5
x
-1/5
15*x^3+2*x^2-75 = -75.04
-1/5
1/5
x
1/5
15*x^3+2*x^2-75 = -74.8
1/5
-1/15
x
-1/15
15*x^3+2*x^2-75 = -74.99555555
-1/15
1/15
x
1/15
15*x^3+2*x^2-75 = -74.98666667
1/15
3/3
x
3/3
15*x^3+2*x^2-75 = -58
3/3
-3/3
x
-3/3
15*x^3+2*x^2-75 = -88
-3/3
3/5
x
3/5
15*x^3+2*x^2-75 = -71.04
3/5
-3/5
x
-3/5
15*x^3+2*x^2-75 = -77.52
-3/5
3/15
x
3/15
15*x^3+2*x^2-75 = -74.8
3/15
-3/15
x
-3/15
15*x^3+2*x^2-75 = -75.04
-3/15
-3/3
x
-3/3
15*x^3+2*x^2-75 = -88
-3/3
3/3
x
3/3
15*x^3+2*x^2-75 = -58
3/3
-3/5
x
-3/5
15*x^3+2*x^2-75 = -77.52
-3/5
3/5
x
3/5
15*x^3+2*x^2-75 = -71.04
3/5
-3/15
x
-3/15
15*x^3+2*x^2-75 = -75.04
-3/15
3/15
x
3/15
15*x^3+2*x^2-75 = -74.8
3/15
5/3
x
5/3
15*x^3+2*x^2-75 = 0
5/3
x-5/3
15*x^2+27*x+45
15*x^3+2*x^2-75
x-5/3
25*x^2-15*x^3
27*x^2-75
45*x-27*x^2
45*x-75
75-45*x
0
15*x^2+27*x+45 = 0
DELTA = 27^2-(4*15*45)
DELTA = -1971
DELTA < 0
x in { 5/3}
2*(x-5/3) = 0
(2*(x-5/3))/(6*x-10) = 0
x-5/3 = 0 // + 5/3
x = 5/3
x in { 5/3}
x belongs to the empty set
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