There is a lot of evidence that the "calories in calories out" approach doesn't work. Research has consistently shown that people on these diets fail to lose the weight or- if they do lose- fail to keep it off. This is because the body is not a static system. It's rate of burning calories does not stay the same. If you reduce calories, the body reduces your metabolism so you burn less calories. If you increase calories, the body increases metabolism to try to burn off the extra calories. The body has a "set weight" that it wants to keep your body weight at. This set weight is regulated by insulin. The more sensitive you are to insulin, the less your body set weight will be. If you are insulin resistant, your body set weight will be higher. This is the reason it's hard for obese people to lose weight. Because their body is always trying to get them to maintain their current weight.
Regaining insulin sensitivity however can lower your body set weight which will make it easier to lose weight. And the easiest way to regain insulin sensitivity is to stop stimulating your insulin response so much. That means cutting out high glycemic index foods like sugar and refined carbohydrates. It means also going periods of time without stimulating insulin, such as through fasting.
Doing a juice fast can be difficult. If you are able to do it, then by all means go ahead. But if you find it tough, you can start small and build up your fasting muscle. Maybe for two weeks you should concentrate on cleaning up your diet and getting rid of processed foods, refined carbohydrates and sugar. Then after that you could move to a 16/8 intermittent fasting schedule. Then after a week or two of that maybe an OMAD (one meal a day) schedule. If you are consistent, you will definitely lose the weight.
I'd recommend taking a look at these videos for inspiration and to learn some of the science behind weight loss and fasting. Id also recommend checking out Dr. Fung's book
The Obesity Code.
Wish you luck on meeting your weight loss goals!