QuadraticsAdvanced
The Quadratic Formula, Explained
When factoring fails, the quadratic formula never does. Learn where it comes from and how to apply it confidently.
Mathew JoaneJune 27, 20268 min read
Every quadratic equation can be written in the standard form below, and the quadratic formula solves any of them — even the ones that refuse to factor.
ax² + bx + c = 0
x = ( -b ± √(b² - 4ac) ) ÷ 2a
Applying it step by step
Consider the equation x² - 3x - 4 = 0. Here a = 1, b = -3, and c = -4.
- 1Compute the discriminant: b² - 4ac = 9 + 16 = 25.
- 2Take the square root: √25 = 5.
- 3Apply the formula: x = (3 ± 5) ÷ 2.
- 4Two solutions: x = 4 or x = -1.
Memorize the formula, but also practice recognizing a, b, and c quickly — that identification step is where most mistakes happen.
Written by Mathew Joane
Algebra teacher on a mission to make math feel less like memorizing and more like understanding.