Eliminate variable x from 2 quadratic equations

Question

The two quadratic equations which I have are

$x^2 - 1970x + 10a =0 $ and

$87x^2 - 3600x + 10b = 0$

I need to eliminate x from these equations such that I get a relation between $a$ and $b$. How shall I do it ?

Answer 1

the equation that will be arrived is $$x=\frac{29a}{5593}-\frac{b}{16779}$$ plugging this in your first equation we get (after simplifications) $${\frac {{b}^{2}}{281534841}}-{\frac {58\,ba}{93844947}}+{\frac {841\,{ a}^{2}}{31281649}}-{\frac {1200\,a}{5593}}+{\frac {1970\,b}{16779}}=0 $$