Solve $LaTeX: \displaystyle 20 x^{2} + 39 x + 18=0$

This is an ac method factoring. The factors of $LaTeX: \displaystyle ac = 360$ that add up to $LaTeX: \displaystyle 39$ are $LaTeX: \displaystyle 24$ and $LaTeX: \displaystyle 15$ . Separating gives $LaTeX: \displaystyle (20 x^{2} + 24 x)+(15 x + 18)=0$ . This gives $LaTeX: \displaystyle (4 x + 3)(5 x + 6)=0$ . The solutions are $LaTeX: \displaystyle x = - \frac{3}{4}$ and $LaTeX: \displaystyle x = - \frac{6}{5}$