I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 2.5 : Quadratic Equations - Part I
4. Solve the following quadratic equation by factoring.
\[19x = 7 - 6{x^2}\]Show All Steps Hide All Steps
Start SolutionThe first thing we need to do is get everything on one side of the equation and then factor the quadratic.
\[\begin{align*}6{x^2} + 19x - 7 & = 0\\ \left( {3x - 1} \right)\left( {2x + 7} \right) & = 0\end{align*}\] Show Step 2Now all we need to do is use the zero factor property to get,
\[\begin{array}{*{20}{c}}{3x - 1 = 0}\\{\displaystyle x = \frac{1}{3}}\end{array}\hspace{0.25in}{\mbox{OR}}\hspace{0.25in}\begin{array}{*{20}{c}}{2x + 7 = 0}\\{\displaystyle x = - \frac{7}{2}}\end{array}\]Therefore the two solutions are : \(\require{bbox} \bbox[2pt,border:1px solid black]{{x = \frac{1}{3}\,\,{\mbox{and }}x = - \frac{7}{2}}}\)
We’ll leave it to you to verify that they really are solutions if you’d like to by plugging them back into the equation.