The sum of twice a triangular number x and its subscript is 24. If their difference is 6, find x?

The x-th triangular number (the triangular number which has x as its subscript) is.

So to answer our question we have to solve the following equation.

Which, after rewriting using the aforementioned formula, ultimately yields the quadratic equation.

Note that we didn't need the condition on the difference between the two numbers, but our solution indeed satisfies it, in fact we have x = 4 and so T(x) = 10, and 10 - 4 = 6.

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