Solve $LaTeX: \displaystyle x^{2} - 15 x + 56=0$

Since $LaTeX: \displaystyle a=1$ we need to find factors of $LaTeX: \displaystyle 56$ that add up to $LaTeX: \displaystyle -15$ . The factors are $LaTeX: \displaystyle -7$ and $LaTeX: \displaystyle -8$ . This gives $LaTeX: \displaystyle (x - 7)(x - 8)=0$ . The solutions are $LaTeX: \displaystyle x = 7$ and $LaTeX: \displaystyle x = 8$