C:\test>junk54 MaunaLoa 636 1
0.011256        -43.244877      41833.442623
Roots: 2093.870 or 1747.905

C:\test>junk54 MaunaLoa 636 2
0.011256        -43.245005      41833.967213
Roots: 2093.804 or 1747.982

C:\test>junk54 MaunaLoa 636 3
0.011256        -43.245005      41833.442623
Roots: 2093.939 or 1747.847

C:\test>junk54 MaunaLoa 636 4
0.011256        -43.245005      41833.967213
Roots: 2093.804 or 1747.982

##</code><code>##

C:\test>junk54 MaunaLoa 636 0
0.011250        -43.220000      41809.395000
Roots: 2093.969 or 1747.809

##</code><code>##

a = 0.01125 
b=-43.33 
c=41809.39500009608 - 636 = 41173.39500009608

b^2 = 1867.9684

4ac = 4 * 0.01125 * 41173.39500009608 = 1852.8027750043236 
[1852.8027750043236]

2a =  0.0225

sqrt( b^2 - 4ac) = sqrt( 1867.9684 - 1852.8027750043236 ) = 3.8943067413438813500081381515803
[3.894306741343881350008138151580260993993447241211454385349751588370799899256543645921436684260125210141335336455851995092334577145331515887188652911540683562874885635121301174306378946428332945435310641569483182791618301871320171448744885624909285788364376693008611415030275581238697717598944067838294453178185116046099184742685399672028363052115485295772994870507036615870130603179788152473302782887122019812566464437007666673563847997186038400782988968755635538]

x' = -b + sqrt(b^2 - 4ac) = 43.22 + 3.8943067413438813500081381515803 = 47.11430674134388135000813815158
[47.1143067413438813500081381515802609939934472412114543853497515883707998992565436459214366842601252101413353364558519950923345771453315158871886529115406835628748856351213011743063789464283329454353106415694831827916183018713201714...]

y' = -b - sqrt(b^2 - 4ac) = 43.22 - 3.8943067413438813500081381515803 = 39.32569325865611864999186184842
[-39.325693258656118649991861848419739006006552758788545614650248411629200100743456354078563315739874789858664663544148004907665422854668484112811347088459316437125114364878698825693621053571667054564689358430516817208381698128679..]

x = x' / 2a = 47.11430674134388135000813815158 / 0.0225 = 2093.9691885041725044448061400702
[2093.96918850417250444480614007023382195526432183162019490443340392759110663362416204095274152267223156183712606470453311521487009534806737276394012940180815834999491711650227441361684206348146424156936184753258590184970230539200761...]

y = y' / 2a = 39.32569325865611864999186184842 / 0.0225 = 1747.8085892736052733329716377076
[1747.8085892736052733329716377075439558225134559461575828733443738501866711441536157368250362551055462159406517130732446625629076824297104050138376483759696194277828606612755033641609357142963135362084159302451918759280754723857...]