Finding the smallest positive integers that satisfies given equations Is it possible to find the smallest positive integer/s that satisfy a given equation or some inequality?
Example:
$2x^2-3x>24$
Is there a formula for this?

This is a very broad question. As for your specific equation, it's equivalent to $a(a-1) = 10b$ so you're basically looking for the smallest pair of successive numbers whose product is a multiple of 10. You also know that you need $a\geq5$ otherwise 5 can't divide $a(a-1)$, so you start looking at 5:
$5\times(5-1)=20=2\times10$. The smallest positive integers that satisfy your equation are $a=5$ and $b=2$.
