1. **State the problem:** A group of people bought a 300 ha farm and shared it equally. The number of hectares per person is 5 less than the number of people. We need to find the number of people. 2. **Define variables:** Let $x$ be the number of people. 3. **Translate the problem into an equation:** Each person gets $\frac{300}{x}$ hectares. According to the problem, this amount is 5 less than the number of people, so: $$\frac{300}{x} = x - 5$$ 4. **Solve the equation:** Multiply both sides by $x$ to clear the denominator: $$300 = x(x - 5)$$ $$300 = x^2 - 5x$$ Rearrange to standard quadratic form: $$x^2 - 5x - 300 = 0$$ 5. **Use the quadratic formula:** For $ax^2 + bx + c = 0$, $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Here, $a=1$, $b=-5$, $c=-300$. Calculate the discriminant: $$\Delta = (-5)^2 - 4(1)(-300) = 25 + 1200 = 1225$$ Calculate the roots: $$x = \frac{5 \pm \sqrt{1225}}{2} = \frac{5 \pm 35}{2}$$ 6. **Find possible values:** - $x = \frac{5 + 35}{2} = \frac{40}{2} = 20$ - $x = \frac{5 - 35}{2} = \frac{-30}{2} = -15$ (not possible since number of people cannot be negative) 7. **Final answer:** The number of people is $\boxed{20}$.