if($a > 0 && $b<0){
   $defb_g  = -$c;
   $defb_gk = g;
}

if($a > 0 && $b<0){
   $defb_g  = -$c;
   $defb_gk = "g";
}

while($klammerterm1 == 0 && klammerterm2 == 0){
 
   dosomething(); 
 

Korrekt wäre:
while($klammerterm1 == 0 && $klammerterm2 == 0){
 
   dosomething(); 
 

function($x, $solution){ 
 . . . 
 . . . 
 if( $with_solution == "1"){
   $x0 = $solution[0];
   $x1 = $solution[1];
   $x2 = $solution[2];
   $x3 = $solution[3];
   $x4 = $solution[4];
 }
}