Quadratic Equation Calculator
Enter a quadratic equation in standard form, e.g. 4x^2-5x-12=0.
Step-by-step method
- Rewrite the equation in standard form ax^2 + bx + c = 0.
- Identify the coefficients a, b, and c.
- Compute the discriminant D = b^2 − 4ac.
- Use the quadratic formula x = (−b ± √D) / (2a).
- Simplify the two solutions.
Example 1: 4x^2-5x-12=0
Step 1 - Rewrite the equation in standard form ax^2 + bx + c = 0.
In this problem: Rewrite 4x^2-5x-12=0 into standard form.
| 4x^2 - 5x - 12 = 0 |
Step 2 - Identify the coefficients a, b, and c.
In this problem: Read off the coefficients from ax^2 + bx + c = 0.
| a = 4 | , | b = -5 | , | c = -12 |
Step 3 - Compute the discriminant D = b^2 − 4ac.
In this problem: Compute the discriminant.
| D | = | ( -5 )^2 | − | 4 | · | 4 | · | ( -12 ) | = | 217 |
Step 4 - Use the quadratic formula x = (−b ± √D) / (2a).
In this problem: Use the quadratic formula with the values found.
| x | = |
|
Step 5 - Simplify the two solutions.
In this problem: Simplify the solutions.
| x | = |
| or | x | = |
|
Final answer: x = 5 + √217/8, x = 5 - √217/8
Example 2: x^2+6x+5=0
Step 1 - Rewrite the equation in standard form ax^2 + bx + c = 0.
In this problem: Rewrite x^2+6x+5=0 into standard form.
| x^2 + 6x + 5 = 0 |
Step 2 - Identify the coefficients a, b, and c.
In this problem: Read off the coefficients from ax^2 + bx + c = 0.
| a = 1 | , | b = 6 | , | c = 5 |
Step 3 - Compute the discriminant D = b^2 − 4ac.
In this problem: Compute the discriminant.
| D | = | 6^2 | − | 4 | · | 1 | · | 5 | = | 16 |
Step 4 - Use the quadratic formula x = (−b ± √D) / (2a).
In this problem: Use the quadratic formula with the values found.
| x | = |
|
Step 5 - Simplify the two solutions.
In this problem: Simplify the solutions.
| x | = | -1 | or | x | = | -5 |
Final answer: x = -1, x = -5
