Who Discovered Quadratic Formula

Believe it or not, people were solving quadratic equations four thousand years ago. The Babylonians didn’t have paper, so they scratched their problems onto clay tablets in cuneiform. They could solve for areas of fields, but they never wrote down a general formula. They just gave recipes like, “Take half of the number, square it, add the constant…” No x’s, no equals signs—just pure, ancient math wizardry.

But here’s the kicker: they only cared about positive answers. Negative numbers? Too depressing. And zero? They thought that was just a placeholder. So if your quadratic had a negative root, they’d shrug and say, “That square doesn’t exist.”

The Greeks get philosophical (and a little lazy)

Then came the Greeks, led by a guy named Euclid. Around 300 BC, Euclid wrote a book called The Elements, which is basically the Bible of geometry. He solved quadratic problems using shapes. Literally, he’d draw squares and rectangles to find the answer. It was beautiful, but also a huge pain. You had to physically cut out paper squares to solve a debt problem. Talk about a math workout.

The Greeks hated negative numbers even more than the Babylonians. They’d rather draw a box around a negative answer than admit it existed. So no formula for them. They just kept drawing.

India: The unsung heroes of algebra

Around 628 AD, an Indian mathematician named Brahmagupta dropped a bombshell. He wrote a book that actually accepted zero and negative numbers as real. He even gave a rule for solving quadratics that sounds eerily familiar: “Multiply the coefficient of the square by the constant, add half the coefficient of the middle term squared…” He was this close to the modern formula.

But Brahmagupta missed one tiny detail: he only worked with positive square roots. So his formula was like a car with only a gas pedal—no reverse. Still, he’s the first person in history to say, “Hey, negative numbers are okay, and here’s how to handle them.” That’s a big deal.

The Middle East: Al-Khwārizmī saves the Day

Fast forward to 820 AD in Baghdad. A Persian scholar named Muhammad ibn Mūsā al-Khwārizmī wrote a book called The Compendious Book on Calculation by Completion and Balancing. Yeah, say that three times fast. He basically invented algebra as we know it, and the word “algorithm” comes from his name. He described the quadratic formula in words, not symbols. He’d say, “If you have a square and ten roots equal thirty-nine, then…” It was a verbal recipe, but it worked.

Al-Khwārizmī still ignored negative roots. But he also gave us the method of “completing the square,” which is the secret sauce inside the formula. Without him, the formula would still be a mess of squiggly lines.

Europe gets in the game (and gets confused)

In the 1100s, European monks translated Al-Khwārizmī’s work from Arabic to Latin, but they made hilarious errors. One translator, Robert of Chester, misread “al-jabr” as “the restoration of a broken bone.” Medieval math was essentially a game of telephone. Still, by the 1500s, European mathematicians like Cardano and Pacioli were solving quadratics, but they still kept the formula a secret. Pacioli actually published a book in 1494 that said, “Quadratic equations are too hard to solve in general.” What a quitter.

The grand prize: Who finally wrote it down?

Here’s the big reveal: the quadratic formula as we know it—the one with the plus-minus sign—was first written in its current symbolic form by Simon Stevin in 1594. Wait, no, that’s not right. Actually, it was René Descartes in 1637? Well, maybe John Wallis in 1685? Historians argue about this like cats fighting over a warm spot. The truth is, the formula evolved slowly. The plus-minus sign (±) didn’t appear until 1841 in a math textbook. Yes, the most iconic part of the formula is younger than the steam engine.

The final version—the one you memorized and then promptly forgot—was popularized by Leonhard Euler in an algebra textbook from 1768. He wrote it in elegant symbols, with all the a, b, c. So if you want to blame one guy, blame Euler. But he also gave us e, the symbol π, and graph theory. He’s basically the Beyoncé of math.

The verdict: no single hero

So who discovered the quadratic formula? A whole army of nerds from four continents, over four thousand years. The Babylonians started it, Brahmagupta pushed it, Al-Khwārizmī named it, and Euler dressed it up in fancy symbols. The formula is a group project where everyone forgot to sign their names.

Next time you use it, give a little nod to a clay tablet in Iraq, a Persian scholar in Baghdad, and a Swiss guy with a big wig. And remember: the plus-minus sign? That’s from the 1800s. You’re welcome.