Find the roots of $3x^2+2x-8=0$ using the quadratic formula.

Step-by-step solution

1. Identify coefficients: $a=3$, $b=2$, $c=-8$.
2. Compute discriminant $D=b^2-4ac=2^2-4(3)(-8)=4+96=100$.
3. Since $D>0$, the roots are real and distinct.
4. Apply the quadratic formula $x=\frac{-b\pm \sqrt{D}}{2a}$.
5. Substitute: $x=\frac{-2\pm 10}{6}$.
6. Simplify: $x=\frac{8}{6}=\frac{4}{3}$ or $x=\frac{-12}{6}=-2$.

Concept tested: Quadratic formula

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