There are two theories of Utility. Cardinal Theory of Utility and Ordinal Theory of Utility. As per Cardinal Utility theory we can assign values or say quantify the utility called 'Utils'. That's how you can get x1 and x2 in terms of 'utils'. We can take any example of utility maximization like spending on fuel and paying house rent. As house rents near my office are very high I would want to go farther so that I can pay lesser rents but then I have to spend more money on fuel. Since I have budget constraints I have to optimize the consumption which is nothing but maximizing utilization for the budget constraints I have.

you take the absolute value of the slope