The quadratic formula is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]first, we need to identify a, b and c.
a is the coefficient that accompanies the squared term, b is the coefficient to the linear term, and c is the constant term.
[tex]a=12;b=-8;c=-9[/tex]then, we replace the formula with the correct values
[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(12)(-9)}}{2(12)}[/tex]simplify the expression
[tex]\begin{gathered} x=\frac{8\pm\sqrt{64+432}}{24} \\ x=\frac{8\pm\sqrt{496}}{24} \\ x=\frac{8}{24}\pm\frac{4\sqrt{31}}{24} \end{gathered}[/tex]divide into the 2 possible answers and simplify the expression
[tex]\begin{gathered} x_1=\frac{1}{3}+\frac{\sqrt{31}}{6} \\ x_2=\frac{1}{3}-\frac{\sqrt{31}}{6} \end{gathered}[/tex]