What are the roots to the following equation? (3x+8)^2=36 a (28)/(3) b -(2)/(3),0 C (2)/(3),(14)/(3) d -(2)/(3),-(14)/(3)

To find the roots of the equation $(3x+8)^{2}=36$, we can start by taking the square root of both sides:<br /><br />$\sqrt{(3x+8)^{2}} = \sqrt{36}$<br /><br />$3x+8 = \pm 6$<br /><br />Now, we can solve for $x$ by isolating it on one side of the equation:<br /><br />$3x+8 = 6$ or $3x+8 = -6$<br /><br />$3x = -2$ or $3x = -14$<br /><br />$x = -\frac{2}{3}$ or $x = -\frac{14}{3}$<br /><br />Therefore, the roots of the equation are $\{ -\frac{2}{3}, -\frac{14}{3}\}$, which corresponds to option d.