Fireworks should explode after
We seek the point (here time
A quadratic function
In our particular fireworks' case we have:
Hence, fireworks should explode after
If the question was 'What height the fireworks will explode at?' we would also have to evaluate the maximum value:
You need to find the height at which the fireworks stop rising and start falling, which you can do by differentiating the equation to find the maximum (the point at which the gradient is zero).