This is a basic quadratic calculator that will give you the roots of a quadratic equation. The output is given in both Radical format and Approximate format (which will actually be exact if the solution is rational, and which will be replaced by NONREAL if it involes non-real numbers), or a nullset if there are no roots.
/quadcalc will open the dialog.
I appologize for the ugliness of the dialog; I originally intended it for my own purposes then later decided to submit it here and didn't feel like redoing the dialog. Maybe I'll get around to it sometime.
--CANT BELIEVE THERES ANOTHER EDIT--
Fixed error where output fields did not clear on consecutive evaluations

dialog quad {
  title "Quadratic Calculator"
  size -1 -1 169 144
  option dbu
  edit "", 1, 2 17 16 10, autohs
  text "Quadratic Calculator", 2, 0 2 168 8, center
  text "x^2+", 3, 19 18 16 8
  edit "", 4, 35 17 16 10, autohs
  text "x+", 5, 51 18 8 8
  edit "", 6, 59 17 16 10, autohs
  text "=0", 7, 75 18 10 8
  button "Evaluate", 9, 130 36 37 12, default
  check "Round", 8, 3 31 29 10
  box "Float Options", 10, 12 40 111 25, disable
  radio "Floor", 12, 15 48 25 10, disable group
  radio "Ceiling", 11, 40 48 29 10, disable
  radio "To", 13, 70 48 16 10, disable
  edit "", 14, 87 48 12 10, limit 2
  text "th digit", 15, 100 49 20 8, disable
  text "Radical", 16, 3 78 20 8
  edit "", 18, 24 77 93 10, read
  text "Approx", 19, 3 108 20 8
  edit "", 20, 24 101 93 10, read
  button "OK", 21, 70 129 37 12, flat ok
  edit "", 40, 24 111 93 10, read
}
alias quadcalc {
  dialog -rm quad quad
}
on *:DIALOG:quad:init:0: {
  did -a quad 1 1
  did -a quad 4 1
  did -a quad 6 0
  did -m quad 14
}
on *:DIALOG:quad:sclick:9,8,13,11,12: {
  if ( $did == 9 ) {
    did -r quad 20
    did -r quad 18
    did -r quad 40
    var %a = $did(quad,1)
    var %b = $did(quad,4)
    var %c = $did(quad,6)
    var %nump = $calc(%b ^ 2 - ( 4 * %a * %c ))
    did -a quad 18 $calc(-1 * %b)) $chr(177) $+(SQRT,$chr(40),%nump,$chr(41)) / $calc(2 * %a)
    if ( %nump == 0 ) {
      did -a quad 20 0
      did -a quad 40 $chr(216)
      halt
    }
    if ( $did(quad,8).state == 1 ) {
      if ( $did(quad,11).state == 1 ) {
        did -a quad 20 $floor($calc((-1 * %b) + $sqrt(%nump) / (2 * %a)))
        did -a quad 40 $floor($calc((-1 * %b) - $sqrt(%nump) / (2 * %a)))
        var %c = 1
      }
      elseif ( $did(quad,12).state == 1 ) {
        did -a quad 20 $ceil($calc((-1 * %b) + $sqrt(%nump) / (2 * %a)))
        did -a quad 40 $ceil($calc((-1 * %b) - $sqrt(%nump) / (2 * %a)))
        var %c = 1
      }
      elseif ( $did(quad,13).state == 1 ) {
        did -a quad 20 $round($calc((-1 * %b) + $sqrt(%nump) / (2 * %a)),$iif($did(quad,14),$did(quad,14),1))
        did -a quad 40 $round($calc((-1 * %b) - $sqrt(%nump) / (2 * %a)),$iif($did(quad,14),$did(quad,14),1))
        var %c = 1
      }
    }
    if ( !%c ) {
      did -a quad 20 $calc((-1 * %b) + $sqrt(%nump) / (2 * %a))
      did -a quad 40 $calc((-1 * %b) - $sqrt(%nump) / (2 * %a))
    }
    .timerf 1 0.1 chd %nump
  }
  elseif ( $did == 8 ) {
    if ( $did(quad,8).state == 1 ) {
      did -be quad 11,12,13,10
      did -c quad 12
      did -u quad 13
      did -u quad 11
    }
    else {
      did -b quad 11
      did -b quad 12
      did -b quad 13
      did -b quad 15
      did -b quad 10
      did -m quad 14
    }
  }
  elseif ( $did == 13 ) {
    if ( $did(quad,13).state == 1 ) {
      did -n quad 14
      did -e quad 15
    }
    else {
      did -m quad 14
      did -b quad 15
    }
  }
  else {
    did -m quad 14
    did -b quad 15
  }
}
alias -l chd {
  if ( !$did(quad,20) ) {
    if ( $left($1,1) != - ) {
      did -a quad 20 NONREAL
      did -a quad 40 NONREAL
    }
    else {
      did -a quad 20 $chr(216)
      did -a quad 40 $chr(216)
    }
  }
}