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use strict;
use warnings;
...
    return if $root < 0;
    return -($b + (0 < $b ? 1 : -1) * sqrt($root)) / 2*$a;
}

a = 4.000000, b = 8.000000, c = 3.000000: -24.000000
a = 2.000000, b = 2.000000, c = 3.000000: No solution
a = -1.000000, b = 2.000000, c = 8.000000: 4.000000