In 5+4/8*9-8+6+5-8+6/24+21/12-5+5+3 you must do the multiplications and divisions ahead of the additions and subtractions: that is, 5+(4/8*9)-8+6+5-8+(6/24)+(21/12)-5+5+3. You do the multiplications and divisions left-to-right so 4/8*9 is 4, divided by 8, result multiplied by 9 (that is, 4.5). You should get 5+4.5-8+6+5-8+0.25+1.75-5+5+3. Now do the additions and subtractions left-to-right, so 5, add 4.5, subtract 8 from total, add 6 to total, ...

A few points to note. 1. PEMDAS (and its friends such as BODMAS) are conventions made up and agreed on by people to communicate mathematical formulae unambiguously with the minimum of effort and maximum of clarity -- see how tedious that formula would be if you had to bracket it fully: ((((((((((5+((4/8)*9))-8)+6)+5)-8)+(6/24))+(21/12))-5)+5)+3). As conventions they can't be right or wrong, merely in use or not in use in a particular context. 2. Not all calculators manage to follow the same conventions as each other, your teacher or your books; nor do they always follow them correctly. For that matter neither do all teachers or books ... 3. A minor point of terminology: you're not solving an equation here, you're computing the value of a formula. There's no equals sign anywhere.