How do I solve this?

Question

7x^2 + 2(sqrt3)xy + 5y^2 = 8

Use a rotation of axes to eliminate the xy-term. (Write an equation in XY-coordinates. Use a rotation angle that satisfies 0 ≤ 𝜑 ≤ 𝜋/2.)

Answer 1

Ax² + Bxy + Cy² + Dx + Ey + F = 0

cot (2θ) = (A - C) / B

Determine θ, sin θ, cosθ

x = x' cos θ - y' sin θ

y = x' sin θ + y' cos θ

Sustitute valus and simplify.