Solve $LaTeX: \displaystyle 8 x^{2} + 30 x + 7=0$

This is an ac method factoring. The factors of $LaTeX: \displaystyle ac = 56$ that add up to $LaTeX: \displaystyle 30$ are $LaTeX: \displaystyle 2$ and $LaTeX: \displaystyle 28$ . Separating gives $LaTeX: \displaystyle (8 x^{2} + 2 x)+(28 x + 7)=0$ . This gives $LaTeX: \displaystyle (2 x + 7)(4 x + 1)=0$ . The solutions are $LaTeX: \displaystyle x = - \frac{7}{2}$ and $LaTeX: \displaystyle x = - \frac{1}{4}$