We use be + adjective + that-clause to express opinions and feelings. Some adjectives commonly used in this way are sure, certain, right, important, afraid, pleased, sorry, surprised, worried. We can omit that with no change in meaning:
It’simportant (that) we look at the problem in more detail.
I’msure (that) you’ll know a lot of people there.
They wereafraid (that) we were going to be late.
Noun + that-clause
We use a noun + that-clause to express opinions and feelings, often about certainty and possibility. We also use that with reporting nouns. Some nouns commonly used in this way are belief, fact, hope, idea, possibility, suggestion, statement, claim, comment, argument:
He is also having intensive treatment in the hopethat he will be able to train on Friday.
Dutch police are investigating the possibilitythat a bomb was planted on the jet.