Solve $LaTeX: \displaystyle 4 x^{2} - 28 x + 45=0$

This is an ac method factoring. The factors of $LaTeX: \displaystyle ac = 180$ that add up to $LaTeX: \displaystyle -28$ are $LaTeX: \displaystyle -10$ and $LaTeX: \displaystyle -18$ . Separating gives $LaTeX: \displaystyle (4 x^{2} - 10 x)+(45 - 18 x)=0$ . This gives $LaTeX: \displaystyle (2 x - 9)(2 x - 5)=0$ . The solutions are $LaTeX: \displaystyle x = \frac{9}{2}$ and $LaTeX: \displaystyle x = \frac{5}{2}$