Solve $LaTeX: \displaystyle 9 x^{2} - 54 x + 80=0$

This is an ac method factoring. The factors of $LaTeX: \displaystyle ac = 720$ that add up to $LaTeX: \displaystyle -54$ are $LaTeX: \displaystyle -24$ and $LaTeX: \displaystyle -30$ . Separating gives $LaTeX: \displaystyle (9 x^{2} - 24 x)+(80 - 30 x)=0$ . This gives $LaTeX: \displaystyle (3 x - 10)(3 x - 8)=0$ . The solutions are $LaTeX: \displaystyle x = \frac{10}{3}$ and $LaTeX: \displaystyle x = \frac{8}{3}$