Okay, so first you set equal to 0:
[tex] 6-6x^{2}=3x\\-6x^{2}-3x+6=0[/tex]
Next simplify the equation so that the leading coefficient is positive:
[tex] \frac{-6x^{2}-3x+6}{-3}=\frac{0}{3}\\2x^{2}+x-2=0[/tex]
Looking at the quadratic equation you can't easily simplify it, so plug it into the quadratic equation and simplify:
[tex] x=\frac{-b\ -+\ \sqrt{b^{2}-4ac}}{2a}\\\\x=\frac{-(1)\ -+\ \sqrt{(1)^{2}-4(2)(-2)}}{2(2)}\\\\x=\frac{-1\ -+\ \sqrt{1+16}}{4}\\\\x=\frac{-1\ -+\ \sqrt{17}}{4}*\frac{-1}{-1}\\\\x=\frac{1\ -+\ \sqrt{17}}{-4},\ or\ B.[/tex]
I noticed a couple mistakes in your work, so if you want me to I can explain them in the comments section :)
