Answer:
D
Step-by-step explanation:
Given the quadratic
d = - 16t² + 12t ← subtract d from both sides
- 16t² + 12t - d = 0 ← in standard form
with a = - 16, b = 12, c = - d
Use the quadratic formula to solve for t
t = ( - 12 ± [tex]\sqrt{12^2-(4(-16)(-d))}[/tex]) / - 32
= ( - 12 ± [tex]\sqrt{144-64d}[/tex]) / - 32
= ( - 12 ± [tex]\sqrt{16(9-4d)}[/tex]) / - 32
= ( - 12 ± 4[tex]\sqrt{9-4d}[/tex]) / - 32
= [tex]\frac{-12}{-32}[/tex] ± [tex]\frac{4}{-32}[/tex][tex]\sqrt{9-4d}[/tex]
= [tex]\frac{3}{8}[/tex] ± [tex]\frac{1}{8}[/tex][tex]\sqrt{9-4d}[/tex]
= [tex]\frac{3}{8}[/tex] ± [tex]\frac{\sqrt{9-4d} }{8}[/tex] → D
