Given an elliptic curve in generalised Weierstrass form

y^2 + a1*xy + a3*y = x^3 + a2*x^2 + a4*x + a6

and a point P=(x,y) which is not the point at infinity.

How exactly do I show that -P is (x, -a1x - a3 - y)?

**Hint: This involves solving a quadratic in y, also the sum of the roots of a monic quadratic polynomial equals the negative of the coefficient of the linear term.

Any help at all would be greatly appreciated.
Cheers, Liedora.