Yes, it is possible. If you have a plan, study at English everyday and can have chance to speak with someone who knows English... you can learn a foreign language. You can search polygots. Poligots learn languages themselves in few months.
I want to give some clues if you are interested in:)
1) Grammar is quite important but for me vocabulary is more important than grammar. Learn vocabulary well and try to use new words that you have just learned in a sentence. So you will remember them easily.
2) Do not think grammar will make you best English speaker. I am 21 years old, in Turkey we start to learn English in 4th class(according to new syllabus, students start in 2nd grade) I have always tried to learn English with grammar and I always failed! :( Last year, I changed my style... I have started to speak without caring about grammar or weak vocabulary. And my language skills have been improved. I couldn't learn English more than 10 years but when I changed my way in learning language, I could speak, write, listen etc in few months!:)
3) Try many ways. When you notice a way is not nice for you.... Change it. Maybe you learn when you read. Or when you listen. But please do not be confused. All skills(listening, speaking, reading, writing) is bounded to each other.
4)Make language learning a part of your life. English or any language must be a part of you and your life.
5)Make language learning funny stuff and be excited when you learn.
I hope this comment will be useful for you.
Love from Turkey to Kazakhistan ^^