Answer
$t=\pm 4i$
Work Step by Step
Step 1: $3t^{2}+45=-3$
Step 2: $3t^{2}=-3-45$
Step 3: $3t^{2}=-48$
Step 4: $t^{2}=-16$
Step 5: Using the square root property, $t=\pm\sqrt {-16}$.
Step 6: $t=\pm\sqrt {-1\times16}$
Step 7: $t=\pm\sqrt {-1}\times\sqrt {16}$
Step 8: $t=\pm i\times4$
Step 9: $t=\pm 4i$
