Twenty times a square of a positive integer plus 50 equals negative 40 times the square of the positive integer plus one-hundred and ten times the positive integer. Which equation could be used to solve for the unknown positive integer.

Let us formulate an expression using the known values in the problem.

Let "x" be the variable that would represent the positive integer.

20X²+50 for the statement "Twenty times a square of a positive integer plus 50"

-40X²+100+10X for the statement "Negative 40 times the square of the positive integer plus one-hundred and 10 times the positive integer".

These two statements are said to be equal such as:

20X²+50=-40X²+100+10X

200X²+40X²-10X+50-100=0

240X²-10X-50=0

The final equation is 240X²-10X-50.