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sqrt(7*x-x^2)*(2*cos(x)-1)=0 equation

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Numerical solution:

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The solution

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   __________                   
  /        2                    
\/  7*x - x  *(2*cos(x) - 1) = 0
$$\sqrt{- x^{2} + 7 x} \left(2 \cos{\left(x \right)} - 1\right) = 0$$
The graph
Rapid solution [src]
x1 = 0
$$x_{1} = 0$$
x2 = 7
$$x_{2} = 7$$
     pi
x3 = --
     3 
$$x_{3} = \frac{\pi}{3}$$
     5*pi
x4 = ----
      3  
$$x_{4} = \frac{5 \pi}{3}$$
x4 = 5*pi/3
Sum and product of roots [src]
sum
    pi   5*pi
7 + -- + ----
    3     3  
$$\frac{5 \pi}{3} + \left(\frac{\pi}{3} + 7\right)$$
=
7 + 2*pi
$$2 \pi + 7$$
product
    pi 5*pi
0*7*--*----
    3   3  
$$\frac{5 \pi}{3} \cdot 0 \cdot 7 \frac{\pi}{3}$$
=
0
$$0$$
0
Numerical answer [src]
x1 = -55.5014702134197
x2 = 11.5191730631626
x3 = 99.4837673636768
x4 = -11.5191730631626
x5 = -42.9350995990605
x6 = -30.3687289847013
x7 = -1.0471975511966
x8 = 0.0
x9 = -89.0117918517108
x10 = -38.7463093942741
x11 = 30.3687289847013
x12 = -49.2182849062401
x13 = -32.4631240870945
x14 = 36.6519142918809
x15 = 38.7463093942741
x16 = 93.2005820564972
x17 = -74.3510261349584
x18 = 74.3510261349584
x19 = 55.5014702134197
x20 = 1.0471975511966
x21 = 51.3126800086333
x22 = 17.8023583703422
x23 = -51.3126800086333
x24 = 95.2949771588904
x25 = 158.126830230686
x26 = -57.5958653158129
x27 = -99.4837673636768
x28 = -82.7286065445312
x29 = 26.1799387799149
x30 = 76.4454212373516
x31 = 57.5958653158129
x32 = 82.7286065445312
x33 = 86.9173967493176
x34 = 24.0855436775217
x35 = -61.7846555205993
x36 = -17.8023583703422
x37 = -26.1799387799149
x38 = 5.23598775598299
x39 = 49.2182849062401
x40 = 45.0294947014537
x41 = 32.4631240870945
x42 = 70.162235930172
x43 = -70.162235930172
x44 = -80.634211442138
x45 = -5.23598775598299
x46 = 89.0117918517108
x47 = -68.0678408277789
x48 = 80.634211442138
x49 = -24.0855436775217
x50 = -95.2949771588904
x51 = -13.6135681655558
x52 = 61.7846555205993
x53 = -162.315620435473
x54 = -93.2005820564972
x55 = 63.8790506229925
x56 = -76.4454212373516
x57 = -63.8790506229925
x58 = 42.9350995990605
x59 = -36.6519142918809
x60 = 68.0678408277789
x61 = -7.33038285837618
x62 = -19.8967534727354
x63 = -45.0294947014537
x64 = 19.8967534727354
x65 = 7.33038285837618
x66 = -86.9173967493176
x67 = 13.6135681655558
x67 = 13.6135681655558