Find the value of $x_1^6 +x_2^6$ of the quadratic equation $25x^2-5\sqrt{76}x+15=0$ without solving it.

I got this question for homework that I have never seen anything similar to it.

Solve for $x_1^6+x_2^6$ for the following quadratic equation where $x_1$ and $x_2$ are the two real roots and $x_1 > x_2$, without solving the equation: $$25x^2-5\sqrt{76}x+15=0 .$$

I tried factoring it, and I got$$(-5x+\sqrt{19})^2-4=0 .$$

What can I do afterwards that does not constitute as solving the equation? Thanks.