[tex]x\text{ = }\frac{-3\pm\sqrt[]{33}}{6}\text{ (option D)}[/tex]Explanation:
3x^2 + 3x = 2
3x^2 + 3x - 2 = 0
The above quadratic equation can't e factorised. We would aplly the almighty formula:
[tex]x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
a = 3, b = 3, c = -2
[tex]\begin{gathered} x\text{ = }\frac{-3\pm\sqrt[]{3^2-4(3)(-2)}}{2(3)} \\ x\text{ = }\frac{-3\pm\sqrt[]{9+24}}{6} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = }\frac{-3\pm\sqrt[]{33}}{6}\text{ } \\ x\text{ = }\frac{-3+\sqrt[]{33}}{6}or\text{ }\frac{-3-\sqrt[]{33}}{6} \\ x\text{ = }\frac{-3\pm\sqrt[]{33}}{6}\text{ (option D)} \end{gathered}[/tex]
