Move all the expressions to the left side of the equation.

Move to the left side of the equation by adding it to both sides.

Move to the left side of the equation by subtracting it from both sides.

Add and .

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

Substitute in the values of , , and .

Simplify each term.

Raising to any positive power yields .

Multiply by .

Multiply by .

Add and .

The nature of the roots of the quadratic can fall into one of three categories depending on the value of the discriminant :

means there are distinct real roots.

means there are equal real roots, or distinct real root.

means there are no real roots, but complex roots.

Since the discriminant is greater than , there are two real roots.

Two Real Roots

Determine the Nature of the Roots Using the Discriminant 0=-2x^2+3