Solver SOLVE quadratic equation (work shown, graph etc)

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Source code of 'SOLVE quadratic equation (work shown, graph etc)'

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==section input
Solve *[input a=1]x2+*[input b=-1]x+*[input c=-2] = 0. You can put negative numbers if you need to use a negative coefficient.

==section solution
perl

my $d = $b*$b-4*$a*$c;

if( $a == 0 ) {
  print "Come on, this is not a quadratic equation!\n";
  return;
}

print "Quadratic equation {{{ax^2+bx+c=0}}} (in our case {{{$a"."x^2+$b"."x+$c = 0}}}) has the following solutons:

{{{x[12] = (b+-sqrt( b^2-4ac ))/2\\a}}}

For these solutions to exist, the discriminant {{{b^2-4ac}}} should not be a negative number.

First, we need to compute the discriminant {{{b^2-4ac}}}: {{{b^2-4ac=($b)^2-4*$a*$c=$d}}}.

my ($x1, $x2);
  my $middle = -$b/2/$a;
  if( $d > 0 ) {
    $x = $x1 = (- $b+sqrt( $d ))/2/$a;
    $x2 = (- $b-sqrt( $d ))/2/$a;
    print "Discriminant d=$d is greater than zero. That means that there are two solutions: {{{ x[12] = (-$b+-sqrt( $d ))/2\\a}}}.

{{{x[1] = (-($b)+sqrt( $d ))/2\\$a = $x1}}}
  {{{x[2] = (-($b)-sqrt( $d ))/2\\$a = $x2}}}
  
  Quadratic expression {{{$a"."x^2+$b"."x+$c}}} can be factored:
{{{$a"."x^2+$b"."x+$c = (x-$x1)*(x-$x2)}}}
";
  } elsif( $d == 0 ) {
    $x = $x1 = $x2 = -$b/2/$a;
    print "Discriminant d=$d is zero! That means that there is only one solution: {{{x = (-($b))/2\\$a}}}.
    Expression can be factored: {{{$a"."x^2+$b"."x+$c = (x-$x1)*(x-$x2)}}}

";
 } else { # d < 0
 my $sd = sqrt( -$d );
 print "The discriminant $d is less than zero. That means that there are no solutions among real numbers. 
If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of $d is + or - {{{sqrt( " . (-$d) . ") = $sd}}}.

The solution is {{{x[12] = (-$b+-i*sqrt( $d ))/2\\$a =  (-$b+-i*$sd)/2\\$a }}}, or
";
  }

if( defined $x1 && defined $x2 ) {
    print "Again, the answer is: $x1, $x2.\n";
  }

print "Here's your graph:\n\n{{{graph( 500, 500, -10, 10, -20, 20, $a*x^2+$b*x+$c )}}}";
==section output
x

==section check
  a=1 b=0 c=0 x1=1