Answer:
[tex]x=\frac{-17+\sqrt{97}}{6}[/tex], [tex]x=\frac{-17-\sqrt{97}}{6}[/tex]
Step-by-step explanation:
Use the quadratic formula to solve for all real solutions.
Quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Plug in and solve:
[tex]x=\frac{-17\pm\sqrt{17^2-4(3)(16)}}{2(3)}\\\\x=\frac{-17\pm\sqrt{289-4(3)(16)}}{2(3)}\\\\x=\frac{-17\pm\sqrt{289-12(16)}}{2(3)}\\\\x=\frac{-17\pm\sqrt{289-192}}{2(3)}\\\\x=\frac{-17\pm\sqrt{97}}{6}\\[/tex]
Since that's the farthest we can simplify to, your answers would be the positive and negative versions of the expression:
[tex]x=\frac{-17+\sqrt{97}}{6}[/tex]
and
[tex]x=\frac{-17-\sqrt{97}}{6}[/tex]
