Solve $LaTeX: \displaystyle 8 x^{2} + 26 x + 15=0$

This is an ac method factoring. The factors of $LaTeX: \displaystyle ac = 120$ that add up to $LaTeX: \displaystyle 26$ are $LaTeX: \displaystyle 6$ and $LaTeX: \displaystyle 20$ . Separating gives $LaTeX: \displaystyle (8 x^{2} + 6 x)+(20 x + 15)=0$ . This gives $LaTeX: \displaystyle (2 x + 5)(4 x + 3)=0$ . The solutions are $LaTeX: \displaystyle x = - \frac{5}{2}$ and $LaTeX: \displaystyle x = - \frac{3}{4}$