Chalana-Kalanabhyam Sutra

We now arrive at a very powerful sutra that forms the basis of calculus in Vedic Mathematics: "Chalana-Kalanabhyam." One of its most well-known uses is for solving quadratic equations, giving us the Vedic equivalent of the famous quadratic formula.

The "Calculus" Rule for Quadratics 📈

For any quadratic equation $ax^2 + bx + c = 0$, this sutra provides a direct formula to find 'x'.

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Example: Solve $x^2 + 5x + 6 = 0$

1. Identify a, b, c: Here, a = 1, b = 5, c = 6.
2. Calculate Discriminant (b² - 4ac): $(5)^2 - 4(1)(6) = 25 - 24 = 1$.
3. Apply the Formula: $x = \frac{-5 \pm \sqrt{1}}{2 \times 1}$.
4. Find the Two Roots:
   • First root: $\frac{-5 + 1}{2} = \frac{-4}{2} = -2$.
   • Second root: $\frac{-5 - 1}{2} = \frac{-6}{2} = -3$.