18=(1/60)*x^2*(36-x)

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Solution for 18=(1/60)*x^2*(36-x) equation: 


x in (-oo:+oo)

18 = (1/60)*x^2*(36-x) // - (1/60)*x^2*(36-x)

18-((1/60)*x^2*(36-x)) = 0

(-1/60)*x^2*(36-x)+18 = 0

18-1/60*x^2*(36-x) = 0

18-1/60*x^2*(36-x) = 0

1/60*x^3-3/5*x^2+18 = 0

1/60*x^3-3/5*x^2+18 = 0

(1/60)*x^3+(-3/5)*x^2+18 = 0

(1/60)*x^3+(-3/5)*x^2+18 = 0 // * 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 8, -8, 9, -9, 10, -10, 12, -12, 15, -15, 18, -18, 20, -20, 24, -24, 27, -27, 30, -30, 36, -36, 40, -40, 45, -45, 54, -54, 60, -60, 72, -72, 90, -90, 108, -108, 120, -120, 135, -135, 180, -180, 216, -216, 270, -270, 360, -360, 540, -540, 1080, -1080 }

1

x = 1

x^3-36*x^2+1080 = 1045

1

-1

x = -1

x^3-36*x^2+1080 = 1043

-1

2

x = 2

x^3-36*x^2+1080 = 944

2

-2

x = -2

x^3-36*x^2+1080 = 928

-2

3

x = 3

x^3-36*x^2+1080 = 783

3

-3

x = -3

x^3-36*x^2+1080 = 729

-3

4

x = 4

x^3-36*x^2+1080 = 568

4

-4

x = -4

x^3-36*x^2+1080 = 440

-4

5

x = 5

x^3-36*x^2+1080 = 305

5

-5

x = -5

x^3-36*x^2+1080 = 55

-5

6

x = 6

x^3-36*x^2+1080 = 0

6

x-6

x^2-30*x-180

x^3-36*x^2+1080

x-6

6*x^2-x^3

1080-30*x^2

30*x^2-180*x

1080-180*x

180*x-1080

0

x^2-30*x-180 = 0

DELTA = (-30)^2-(-180*1*4)

DELTA = 1620

DELTA > 0

x = (1620^(1/2)+30)/(1*2) or x = (30-1620^(1/2))/(1*2)

x = (18*5^(1/2)+30)/2 or x = (30-18*5^(1/2))/2

x in { (30-18*5^(1/2))/2, (18*5^(1/2)+30)/2, 6} 

(x-((30-18*5^(1/2))/2))*(x-((18*5^(1/2)+30)/2))*(x-6) = 0

(x-((30-18*5^(1/2))/2))*(x-((18*5^(1/2)+30)/2))*(x-6) = 0

( x-((18*5^(1/2)+30)/2) )

x-((18*5^(1/2)+30)/2) = 0 // + (18*5^(1/2)+30)/2

x = (18*5^(1/2)+30)/2

( x-((30-18*5^(1/2))/2) )

x-((30-18*5^(1/2))/2) = 0 // + (30-18*5^(1/2))/2

x = (30-18*5^(1/2))/2

( x-6 )

x-6 = 0 // + 6

x = 6

x in { (18*5^(1/2)+30)/2, (30-18*5^(1/2))/2, 6 }

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