Solving Quadratic Equations using the Quadratic Formula

The Quadratic Formula has many computations and, therefore, many places where errors can occur. In this case we can see that the first time $b=\text{-}7$ was replaced in the Quadratic Formula, one of the negatives was dropped. $$\begin{array}{ccc}x& =& \frac{\text{-}b\pm \sqrt{b^2-4ac}}{2a}\end{array}$$ In our quadratic, $3x^2-7x-6=0,$ we have $a=3,$ $b=\text{-}7,$ and $c=\text{-}6.$ So the first substitution of $\text{-}b$ should have looked like $\text{-}(\text{-}7).$

Let's substitute correctly and solve.

Interestingly enough, the answers with the error are just different signs of the actual solutions.