Solve $LaTeX: \displaystyle 20 x^{2} - 67 x + 56=0$

This is an ac method factoring. The factors of $LaTeX: \displaystyle ac = 1120$ that add up to $LaTeX: \displaystyle -67$ are $LaTeX: \displaystyle -35$ and $LaTeX: \displaystyle -32$ . Separating gives $LaTeX: \displaystyle (20 x^{2} - 35 x)+(56 - 32 x)=0$ . This gives $LaTeX: \displaystyle (5 x - 8)(4 x - 7)=0$ . The solutions are $LaTeX: \displaystyle x = \frac{8}{5}$ and $LaTeX: \displaystyle x = \frac{7}{4}$