Solve $LaTeX: \displaystyle 20 x^{2} + x - 1=0$

This is an ac method factoring. The factors of $LaTeX: \displaystyle ac = -20$ that add up to $LaTeX: \displaystyle 1$ are $LaTeX: \displaystyle -4$ and $LaTeX: \displaystyle 5$ . Separating gives $LaTeX: \displaystyle (20 x^{2} - 4 x)+(5 x - 1)=0$ . This gives $LaTeX: \displaystyle (4 x + 1)(5 x - 1)=0$ . The solutions are $LaTeX: \displaystyle x = - \frac{1}{4}$ and $LaTeX: \displaystyle x = \frac{1}{5}$