Answer
$x=\left\{
-\dfrac{8}{3}, 1
\right\}
$
Work Step by Step
Using the properties of equality, the given equation, $
3x^2+5x=8
,$ is equivalent to
\begin{align*}
3x^2+5x-8&=8-8
\\
3x^2+5x-8&=0
.\end{align*}
Using $ax^2+bx+c=0,$ the equation above has $a=
3
,$ $b=
5
,$ and $c=
-8
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}
x&=\dfrac{-5\pm\sqrt{5^2-4(3)(-8)}}{2(3)}
\\\\&=
\dfrac{-5\pm\sqrt{25+96}}{6}
\\\\&=
\dfrac{-5\pm\sqrt{121}}{6}
\\\\&=
\dfrac{-5\pm11}{6}
\end{align*}
\begin{array}{lcl}
x=\dfrac{-5-11}{6} &\text{ OR }& x=\dfrac{-5+11}{6}
\\\\
x=\dfrac{-16}{6} && x=\dfrac{6}{6}
\\\\
x=-\dfrac{8}{3} && x=1
.\end{array}
The solutions are $
x=\left\{
-\dfrac{8}{3}, 1
\right\}
.$
