Anumber multiplied by itself added to itself equals 30. what are the two possible numbers?

The number . . . x

Multiplied by itself . . . x²

Multiplied by itself, then added to itself . . . x² + x

You said it's equal to 30, so            x² + x = 30  .

Subtract  30  from each side:      x² + x - 30 = 0   .

There you have a perfectly nice quadratic equation.
To solve it, you can either factor the left side, or use the quadratic equation.
Either way, the two solutions are

             x = 5
and
             x = -6 .