The solution of a quadratic equation is a pair of numbers - let's call them a and b [assume a smaller than or equal to b].
The solution of a quadratic inequality is EITHER all the numbers between a and b, OR
all the numbers less than a AND all the numbers greater than b.
To UNsolve a quadratic equation or inequality, drag the GREEN dots in the left hand panel to fix the solution set. The right hand panel will show you a quadratic equation or inequality that has that solution set.
You can drag the GOLD dots in the right hand panel to see other quadratic equations or inequalities that have the same solution set.
For a given solution set, how many equations or inequalities are there that have that solution set? How do you know? Can you prove it?