To set up the equation given the information:
Let \( a \) represent last year's budget for the winter dance.
According to the problem, the school plans to spend twice last year's budget minus the cost of the disco ball which is $150. The total amount being spent this year is $1,500.
We can write the equation as follows:
\[ 2a - 150 = 1500 \]
This equation represents the relationship described in the problem.