```
:a+bi
:Prompt A,B,C,D,E
:(8AC-3(B^2))/(8(A^2))→G
:((B^3)+8D(A^2)-4ABC)/(8(A^3))→H
:(C^2)-3BD+12AE→I
:2(C^3)-9BCD+27(B^2)E+27A(D^2)-72ACE→J
:cuberoot((J+squareroot((J^2)-4(I^3)))/2)→K
:0.5squareroot((-2/3)G+(1/(3A))(K+(I/K)))→L
:(-B/(4A))-L+0.5squareroot(-4(L^2)-2G+(H/L))→M
:(-B/(4A))-L-0.5squareroot(-4(L^2)-2G+(H/L))→N
:(-B/(4A))+L+0.5squareroot(-4(L^2)-2G-(H/L))→P
:(-B/(4A))+L-0.5squareroot(-4(L^2)-2G-(H/L))→Q
:Disp "ROOTS ARE",M
:Disp N
:Disp P
:Disp Q
```

Pretty cool, you should try a quintic equation silver ;) I don't have my calc to test, but I think I can optimize!

```
:a+bi
:ClrList L1
:Prompt A,B,C,D,E
:2C-3B²/(4A²→G
:DAֿ¹+(B³-4ABC)/(8A³→H
:C²-3BD+12AE→I
:2C³-9(BCD-3B²E-3AD²+8ACE
:³√(.5(Ans+√(Ans²-4I³
:ö3ֿ¹(-G+Aֿ¹(Ans+I/Ans→I
:2H/√(Ans→C
:-B/(4A→A
.5√(-I-G+C→B
.5√(-I-G-C
:Disp "ROOTS ARE",A-C+B,A-C-B,A+C+Ans,A+C-Ans
```

Nevermind the ö, I was just running into an odd formatting error with the inverse token.

Z80 Assembly>English>TI-BASIC>Python>French>C>0

One thing I've been meaning to do is remove the ClrList L1. I originally stored the roots to a list, but I didn't like the way a list displayed complex roots, so I had it stored to regular variables, but forgot to remove the ClrList. I'll go ahead and do that while I'm thinking about it.

As for a quintic equation solver, I may create one, but I'm pretty sure the PLYSMITH app (I think that's what it is called) already has one.

Just did some research on Quintic Equation Solvers, and there's no formula like that for quadratics, cubics, and quartics. I don't think I'll create a program for quintics, since it doesn't sound like it is worth my time and effort.

Haha, nope! It's really cool that there are only formulas up to quartic.

Z80 Assembly>English>TI-BASIC>Python>French>C>0

I think it is somewhat ridiculous that if formulas for ordered polynomials of orders 2, 3, and 4 exist, then why don't 5 and higher exist? I guess it just shows that we can't know everything about Creation.

It was mathematically proven (to some surprise) by Evariste Galois using what is now known as Galois theory.

It makes sense in the way that we can find integer solutions for a+b=c, a^2+b^2=c^2, but there are no solutions for any higher powers. It's a property of numbers the way we defined them.

Z80 Assembly>English>TI-BASIC>Python>French>C>0

where is the cuberoot and squareroot commands??

Square Root is [2nd] then $x^2$

Cube Root is [2nd] then 0 then 3 then scroll to the bottom. When the arrow points to Cube Root, press enter.

Is the cube root token also found at `[math][4]`? I don't have my calc on me.

Z80 Assembly>English>TI-BASIC>Python>French>C>0