How to tell if a quadratic equation has a real solution?

The easiest way to determine if a quadratic equation has real solutions is by using the discriminant.

Start by finding a, b and c. You can find a by looking at the coefficient of x^2. You can find b by looking at the coefficient of x. You can find c by looking at the constant at the end.

Now use the discriminant formula.

b^2 - 4ac

After plugging in and solving, check the number. If it is negative, there are no real solutions. If it is positive there are 2 solutions. If it is 0, there is one real answer and it is a double root.

If the discriminant (b^2-4ac) is rational, then the quadratic is rational.

~ThePirc