Question: How to solve the problem of least square ?

i need to solve the equation in method in least square; i have one equation e.g.f(x)=a*x^2-b*x-c, but i need use it two times in one equation,like g(x)=f(x1)-f(x). f(x1) put the value x1 in equation f(x),the behind is not change.so the equation like this : a*x1^2-b*x1-c-a*x^2-b*x-c if i input the equation g(x):=f(x)-f(x)the input the value a,b,c.got the 0. it's not my need. who can tell me how to solve the problem?
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