While solving quadratic equations, it’s useful to take a look at the discriminant.

The discriminant is area under the square root in the quadratic formula:

if you have a quadratic equation (equation equal to zero with 3 distinct parts), you can use the quadratic formula to solve. Depending on the answer, we can figure out whether the equation will have 1,2 or 0 solutions.

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Let’s find the discriminant of the equation:

In a quadratic equation, the parent would be

following the parent, in our equation, a=1, b=-3, and c=6

using this information we can plug in the numbers to our equation to find the discriminant.

If is our equation, we just put our numbers we found in the spots of the letters, and simplify.

using this we know that since the discriminant is -15, the original quadratic equation does not have any solutions, and using the quadratic formula would not work.