The way to answer (a) is to show why, if the mean of x numbers is x-3, and their sum is 70, then x^2 - 3x - 70 = 0. To do that, write an expression for the sum of the numbers if there are x of them and their mean is x-3, and set that equal to 70. This will not involve the factors you wrote.
Then, one way to answer (b) is to factor the equation from (a), which turns out to be similar to (x-7) (x+10)=0. Solve the correctly factored equation for x. (Always check your factoring by multiplication.)
It may help the mean of x numbers is the arithmetic mean, otherwise known as the average. And their total is 70 means that when you add those numbers together that you are finding the average of, you get 70.