Answer: Delphiniums are short-lived perennials in your gardening region. The normal course of events is to plant seed in October for bloom in late spring and early summer. I suspect your plants will resprout and bloom for you next spring. If you cut the flower spikes down when the flowers are spent, the plant should send up additional (although shorter) flowering spikes. If you allow the first flowers to remain, they will set seed which you can collect and plant, or which will fall down onto the soil for germination the following season.
For now, cut back the foliage and stems and wait to see what happens in the spring.
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