After finding the discriminant of a quadratic equation, the next steps to solve the equation using the quadratic formula are as follows:
1. Determine the value of the discriminant (denoted as Δ) by substituting the coefficients of the quadratic equation into the formula: Δ = b^2 - 4ac.
2. Based on the value of the discriminant:
a. If Δ > 0 (positive discriminant), the equation has two distinct real roots.
b. If Δ = 0 (zero discriminant), the equation has one real root (a perfect square trinomial).
c. If Δ < 0 (negative discriminant), the equation has no real roots (complex roots).
3. Once you know the nature of the roots, you can proceed with the quadratic formula, which is:
x = (-b ± √Δ) / 2a
Here, the ± symbol indicates that you will have two solutions, one with a positive sign (+) and the other with a negative sign (-).
4. Substitute the values of a, b, and Δ you obtained from the quadratic equation into the quadratic formula.
5. Simplify the expression by performing the necessary operations, such as addition, subtraction, multiplication, and division.
6. Calculate the values of x by evaluating the positive and negative solutions separately. This will give you the two possible solutions for the quadratic equation.
7. Express the final solutions in decimal or fraction form, depending on the given quadratic equation.
These steps will guide you in solving a quadratic equation using the quadratic formula after finding the discriminant.