I´ve found a strange and difficult to prove formula that derived from two quadratic equations.

"If two quadratic equations: and share one solution.

then: .......(1) is always true."

If they are equivalent, It is known that their coefficients are proportional: .

since the two quadratic equations above share just one solution, I suppose they are partially equivalent.

I've been trying to prove the formula in (1). I apologize for the lack of content about the problem.

Any suggestion will be appreciated.