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

"If two quadratic equations:$\displaystyle Ax^2+Bx+C=0$ and $\displaystyle Dx^2+Ex+F=0$ share one solution.

then: $\displaystyle (CD-FA)^2=(BF-EC)(AE-BD)$.......(1) is always true."

If they are equivalent, It is known that their coefficients are proportional:$\displaystyle \frac{A}{D}=\frac{B}{E}=\frac{C}{F}$.

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.