Solving Quadratic Equations Using the Quadratic
Formula
To use the quadratic formula to solve a quadratic equation, we replace a,
b, and c with specific numbers. Then we simplify the resulting expression.
Procedure â€” To Solve a Quadratic Equation Using the Quadratic Formula
Step 1 Write the quadratic equation in standard form,
ax^{2} + bx + c = 0.
Step 2 Identify the values of a, b, and c.
Step 3 Substitute the values of a, b, and c into the
quadratic formula.
Step 4 Simplify.
Step 5 Check each solution.
Example 1
Solve using the quadratic formula: 3x^{2}  16x = 5
Solution
Step 1 Write the quadratic equation in standard form,
ax^{2} + bx + c = 0. Add 5 to both sides of the equation.
Step 2 Identify the values of a, b, and c. 

Step 3 Substitute the values of a,
b, and c into the quadratic
formula. 

Step 4 Simplify. 

Step 5 Check each solution.
We leave the check to you.


The two solutions of 3x^{2}  16x = 5 are
and 5.
