Let's solve this by using the quadratic formula:
[tex]\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
Note that we only use the coefficients so a=12, b=-14, and c=-6.
Plug values in the quadratic equation:
[tex] \frac{ - ( - 14)± \sqrt{ {( - 14)}^{2} - 4(12)( - 6) } }{2(12)} [/tex]
And so by evaluating those values we obtain:
[tex]\frac{14+-\sqrt{484} }{24}=\frac{14+-22}{24} \\\\[/tex]
Now we have two answers which are our factors one where we add another where we subtract and so:
First factor:
[tex]\frac{14+22}{24}=\frac{36}{24}=\frac{3}{2}[/tex]
Second Factor:
[tex]\frac{14-22}{24}=\frac{-8}{24}=-\frac{1}{3}[/tex]
And so your factors are
[tex]\frac{3}{2},-\frac{1}{3}[/tex]
meaning that those are your roots/x-intercepts.
