The "no thinking required" way to solve it is using the quadratic formula. That formula tells you the solution to
[tex]ax^2+bx+c=0[/tex]
is given by
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Your equation has a=-2, b=3, c=-9, so the solution is
[tex]x=\dfrac{-3\pm \sqrt{3^2-4\cdot (-2)\cdot (-9)}}{2\cdot (-2)}\\\\=\dfrac{3\pm \sqrt{9-72}}{4}=\dfrac{3\pm 3\sqrt{-7}}{4}\\\\x=\dfrac{3}{4}\pm i\dfrac{3\sqrt{7}}{4}[/tex]
The solutions are complex numbers.
