Example 2: Solve $3x^2+x-14=0$ for $x$ using the Quadratic Formula. 
Solution: This method works for any quadratic. First, identify $a,\ b,\ \text{and } c$. $a$ equals the number of $x^2$ terms, $b$ equals the number of $x$ terms, and $c$ equals the constant. For $3x^2+x-14=0$, $1=3,\ b=1,\ \text{and } c=-14$. Substitute the values of $a,b,\text{and } c$ into the Quadratic Formula and evaluate the expression twice: once with addition and once with subtraction. Examine this method below:

$x=\frac{-1+\sqrt{1^2-4(3)(-14)}}{2\cdot3} \\ =\frac{-1+\sqrt{169}}{6} \\ =\frac{12}{6}=2$     or      $x=\frac{-1-\sqrt{1^2-4(3)(-14)}}{2\cdot3} \\ =\frac{-1-\sqrt{169}}{6} \\ =\frac{-14}{6}=-\frac{7}{3}$