Solve $LaTeX: \displaystyle 20 x^{2} + 53 x + 35=0$

This is an ac method factoring. The factors of $LaTeX: \displaystyle ac = 700$ that add up to $LaTeX: \displaystyle 53$ are $LaTeX: \displaystyle 25$ and $LaTeX: \displaystyle 28$ . Separating gives $LaTeX: \displaystyle (20 x^{2} + 25 x)+(28 x + 35)=0$ . This gives $LaTeX: \displaystyle (5 x + 7)(4 x + 5)=0$ . The solutions are $LaTeX: \displaystyle x = - \frac{7}{5}$ and $LaTeX: \displaystyle x = - \frac{5}{4}$