Answer
{$-1.61,2.28$}
Work Step by Step
Step 1: Comparing $-3x^{2}+2x+11=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$, we obtain:
$a=-3$, $b=2$ and $c=11$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$
Step 3: Substituting the values of a, b and c in the formula:
$x=\frac{-(2) \pm \sqrt {(2)^{2}-4(-3)(11)}}{2(-3)}$
Step 4: $x=\frac{-2 \pm \sqrt {4+132}}{-6}$
Step 5: $x=\frac{-2 \pm \sqrt {136}}{-6}$
Step 6: $x=\frac{-2 \pm 11.662}{-6}$
Step 7: $x=\frac{-2 + 11.662}{-6}$ or $x=\frac{-2 - 11.662}{-6}$
Step 8: $x=\frac{9.662}{-6}$ or $x=\frac{-13.662}{-6}$
Step 9: $x=-1.610\approx-1.61$ or $x=2.277\approx2.28$
Step 10: Therefore, the solution set is {$-1.61,2.28$}.
