#### Answer

$x=\pm2\sqrt{6}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
3x^2+8=80
,$ use the properties of equality and express the equation in the form $x^2=c.$ Then take the square root of both sides (Square Root Property) and simplify the resulting radical.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
3x^2=80-8
\\\\
3x^2=72
\\\\
x^2=\dfrac{72}{3}
\\\\
x^2=24
.\end{array}
Taking the square root of both sides (Square Root Property), the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=\pm\sqrt{24}
.\end{array}
Writing the radicand as an expression that contains a factor that is a perfect power of the index and then extracting the root of that factor result to
\begin{array}{l}\require{cancel}
x=\pm\sqrt{4\cdot6}
\\\\
x=\pm\sqrt{(2)^2\cdot6}
\\\\
x=\pm2\sqrt{6}
.\end{array}