1. --To use this, simply write the following at the very end: 'Solve(a,b,c)' [where a,b,c are Integers.]
2. --Example: Solve(1,-2,3)
3. --It solves the following equation: ax^2 + bx + c = 0.
4. --After writing, execute the code.
5. --It outputs the answers in the form of square roots and fractions, instead of decimals.
6. --It also gives other information about the equation made from the input.
7.  
8. function FP(numbers)
9. if #numbers>0 then
10. local F = {}
11.  for k=1, #numbers do
12.  local n = numbers[k]
13.  local n2 = math.abs(n)
14.  local f = {{1,1}}
15.  if n2 ~= 1 then
16.  while n2>1 do
17.   for i=2, math.abs(n) do
18.    if n2>1 then
19.     if math.floor(n2/i)==n2/i then
20.     local lol = 1
21.      while lol >= 1 do
22.      local LOL = i^(lol+1)
23.       if math.floor(n2/LOL)~=n2/LOL then
24.        f[#f+1] = {i,lol}
25.        n2 = n2/(i^lol)
26.        lol = 0
27.       else
28.        lol = lol+1
29.       end
30.      end
31.     end
32.    end      
33.   end
34.  end
35.  end
36.  F[#F+1]=f
37.  end
38. return F
39. end
40. end
41. function FCF(pon)
42.  local af = FP({pon[1]})
43.  local bf = FP({pon[2]})
44.  local cf = {{1,1}}
45.  for i=1, #af[1] do
46.   for k=1, #bf[1] do
47.    local f1 = af[1][i]
48.    local f2 = bf[1][k]
49.    local s = nil
50.    if f1[1]==f2[1] then
51.     if f1[2] >= f2[2] then
52.      s=f2[2]
53.     elseif f1[2] < f2[2] then
54.      s=f1[2]
55.     end
56.     cf[#cf+1]={f1[1],math.abs(s)}
57.    end
58.   end
59.  end
60.  return cf
61. end
62. function ECF(pon2)
63.  local f = FCF(pon2)
64.  local cf=1
65.  for i=1, #f do
66.  cf = cf*(f[i][1]^f[i][2])
67.  end
68.  return cf
69. end
70. function Solve(a,b,c)
71. local result = nil
72. if tonumber(a)~=nil and tonumber(b)~=nil and tonumber(c)~=nil then
73. if a == math.floor(a) and b == math.floor(b) and c == math.floor(c) then
74. if a ~= 0 then
75. local t = 1
76. local s = {}
77. local S = 1
78. local D = (b*b)-(4*a*c)
79.  if D<0 then
80.  t=-1
81.  end
82.  if math.abs(D)>0 then
83.   local Df = FP({D})
84.   for k1=1, #Df[1] do
85.    local f = Df[1][k1]
86.    if f[2] == 1 then
87.     t=t*f[1]
88.    elseif f[2]/2 ~= math.floor(f[2]/2) and f[2]>1 then
89.     f[2]=f[2]-1
90.     s[#s+1]=f[1]^f[2]
91.     t=t*f[1]
92.    elseif f[2]/2 == math.floor(f[2]/2) then
93.     s[#s+1]=f[1]^f[2]
94.    end
95.   end
96.   for k2=1, #s do
97.   S = S*math.sqrt(s[k2])
98.   end
99.   if t~=1 then
100.    local ncf = ECF({b,S})
101.    local fcf = ECF({2*a,ncf})
102.    n1 = ((-1*b)/fcf)
103.    n2 = (S/fcf)
104.    d = (2*a/fcf)
105.    if n1 == 0 then
106.    local fcf4 = ECF({2*a,S})
107.    n2 = S/fcf4
108.    d = 2*a/fcf4
109.    end
110.   end
111.  elseif D == 0 then
112.  t=0
113.  end
114.  if t == 0 then
115.   local fcf1 = ECF({b,2*a})
116.   local n = b/fcf1
117.   local da = 2*a/fcf1
118.    if math.abs(da) ~= 1 and math.abs(da) ~= math.abs(n) then
119.     result = "SOLUTION: "..tostring(-1*n).."/"..tostring(da).." | FACTORABLE | 1 REAL SOLUTION"
120.    else
121.     result = "SOLUTION: "..tostring(-1*n/da).." | FACTORABLE | 1 REAL SOLUTION"
122.    end
123.   elseif t>1 then
124.   if n2 == 1 then
125.   n2 = ""
126.   end
127.   if n1 ~= 0 then
128.   result = "SOLUTIONS: ("..tostring(n1).." + "..tostring(n2).."sqrt("..tostring(t).."))/"..tostring(d).." and ("..tostring(n1).." - "..tostring(n2).."sqrt("..tostring(t).."))/"..tostring(d).." | NOT FACTORABLE | 2 REAL SOLUTIONS"
129.   elseif n1 == 0 then
130.   result = "SOLUTIONS: "..tostring(n2).."sqrt("..tostring(t)..")/"..tostring(d).." and (-"..tostring(n2).."sqrt("..tostring(t).."))/"..tostring(d).." | NOT FACTORABLE | 2 REAL SOLUTIONS"
131.   end
132.   elseif t<0 then
133.   if n2 == 1 then
134.    n2 = ""
135.   end
136.   t=math.abs(t)
137.   if n1 ~= 0 then
138.    if t ~= 1 then
139.    result = "SOLUTIONS: ("..tostring(n1).." + "..tostring(n2).."sqrt("..tostring(t)..")i)/"..tostring(d).." and ("..tostring(n1).." - "..tostring(n2).."sqrt("..tostring(t)..")i)/"..tostring(d).." | NO REAL SOLUTIONS"
140.    elseif t ==1 then
141.    result = "SOLUTIONS: ("..tostring(n1).." + "..tostring(n2).."i)/"..tostring(d).." and ("..tostring(n1).." - "..tostring(n2).."i)/"..tostring(d).." | NO REAL SOLUTIONS"
142.    end
143.   elseif n1 == 0 then
144.    if t ~= 1 then
145.    result = "SOLUTIONS: "..tostring(n2).."sqrt("..tostring(t)..")i)/"..tostring(d).." and (-"..tostring(n2).."sqrt("..tostring(t)..")i)/"..tostring(d).." | NO REAL SOLUTIONS"
146.    elseif t ==1 then
147.    result = "SOLUTIONS: "..tostring(n2).."i/"..tostring(d).." and (-"..tostring(n2).."i)/"..tostring(d).." | NO REAL SOLUTIONS"
148.    end
149.   end
150.  elseif t==1 then
151.   local fcf2 = ECF({2*a,(-b)+S})
152.   local fcf3 = ECF({2*a,b+S})
153.   local n1a = (((-b)+S)/fcf2)
154.   local n2a = ((b+S)/fcf3)
155.   local db1 = (2*a/fcf2)
156.   local db2 = (2*a/fcf3)
157.    if math.abs(db) ~= 1 then
158.     result = "SOLUTIONS: "..tostring(n1a).."/"..tostring(db1).." and ".."("..tostring(-1*n2a)..")/"..tostring(db2).." | FACTORABLE | 2 REAL SOLUTIONS"
159.    else
160.     result = "SOLUTIONS: "..tostring(n1a/db1).." and "..tostring(-1*n2a/db2).." | FACTORABLE | 2 REAL SOLUTIONS"
161.    end
162.  end
163.  elseif a == 0 and b ~= 0 then
164.  local lcf = ECF({b,c})
165.  local ln = -c/lcf
166.  local ld = b/lcf
167.  if math.abs(ld) ~= 1 and math.abs(ld) ~= math.abs(c) and ln ~= 0 then
168.  result = "SOLUTION: "..tostring(ln).."/"..tostring(ld).." | This is a linear equation."
169.  else
170.  result = "SOLUTION: "..tostring(ln/ld).." | This is a linear equation."
171.  end
172.  elseif a==0 and b == 0 then
173.  result = "NO SOLUTIONS | This is a constant..."
174.  if c == 0 then
175.  result = "SOLUTION: ANY NUMBER | What equation is this?"
176.  end
177.  end
178. else
179.   result = "This program only works on integers :("
180. end
181. else
182.  result = "Please check your input, it must be in the form of Solve(INTEGER,INTEGER,INTEGER)"
183. end
184. print(result)
185. end
186. --Example--------------
187. Solve(2,3,5)
188. ------------Remove this