# What are the different methods for solving quadratic equations?

Example: Solve: $y = 16 {x}^{2} - 62 x + 21 = 0$.
Solve the transformed equation $y ' = {x}^{2} - 62 x + 336 = 0$. Compose factor pairs of (ac = 336) --> ...(4, 82)(6, 56). This last sum is 62 = -b. Then, the 2 real roots of y' are: 6 and 56.
The 2 real roots of original y are: $x 1 = \frac{6}{a} = \frac{6}{16} = \frac{3}{8}$, and
$x 2 = \frac{56}{a} = \frac{56}{16} = \frac{7}{2}$