What are the approximate solutions of 2x^2-x+10=0?

Notice that the discriminant is - 79. So there are no real solutions.

The discriminant is (b^2-4ac) of the quadratic formula.

The rule:

If the discriminant is less than zero there are no real solutions (though there are two imaginary ones).

If the discriminant is greater than zero there are two real solutions.

If the discriminant is equal to zero there is only one solution.