Example 2: Solve $3x^2+x-14=0$ for $x$ using the Quadratic Formula.

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

$\begin{array}{l} x = \frac{-1 + \sqrt{1^2 - 4 \left(3\right) \left(-14\right)}}{2 \cdot 3} \\ \phantom{x} = \frac{-1 - \sqrt{169}}{6} \\ \phantom{x} = \frac{12}{6} \\ \phantom{x} = 2 \end{array} \quad \text{or} \quad \begin{array}{l} x = \frac{-1 + \sqrt{1^2 - \left(3\right) \left(-14\right)}}{2 \cdot 3} \\ \phantom{x} = \frac{-1 - \sqrt{169}}{6} \\ \phantom{x} = \frac{-14}{6} \\ \phantom{x} = -\frac{7}{3} \end{array}$