Expressing “to discuss" with 讨论 and 谈论
Both verbs have similar meanings. The verb 讨论 means “to discuss” and the verb 谈论 means “to talk about”.
The verb 讨论
The verb 讨论 
expresses a discussion of something in a formal setting.
expresses a discussion of something in a formal setting.Examples
她不愿讨论这部话剧的内容
She doesn’t want to discuss the summary of the play
tā bú yuàn tǎolùn zhè bù huàjù de nèiróng
我们分组讨论了那个问题
We were discussing it in groups
wǒmen fēnzǔ tǎolùn le nà ge wèntí
他们在讨论西方社会的问题
They are discussing the problems of western society
tāmen zhèngzài tǎolùn xīfāng shèhuì de wèntí
讨论 as a noun
讨论 can also be a noun in the meaning of “discussion”.
Examples
两位领导仍在进行讨论
The two leaders are still holding a discussion
liǎng wèi lǐngdǎo réng zài jìnxíng tǎolùn
讨论变得有点严肃
The discussion has become more serious
tǎolùn biàn de yǒudiǎn yánsù
The verb 谈论
The verb 谈论 expresses the discussion of something in an informal setting.
expresses the discussion of something in an informal setting.Examples
我们整个晚上谈论家庭琐事
We spent the whole evening talking about the household chores
wǒmen zhěnggè wǎnshàng tánlùn jiātíng suǒshì
你们在谈论什么呢？
What are you talking about?
nǐmen zài tánlùn shénme ne
我不想在电话里谈论此事
I don’t want to talk about it on the phone
wǒ bù xiǎng zài diànhuà lǐ tánlùn cǐ shì