Answer
$\{-\frac{1}{3},2\}$.
Work Step by Step
$3x^2=5x+2$
Add $-5x-2$ to both sides.
$3x^2-5x-2=5x+2-5x-2$
Simplify.
$3x^2-5x-2=0$
Rewrite the middle term $-5x$ as $-6x+x$.
$3x^2-6x+x-2=0$
Group terms.
$(3x^2-6x)+(x-2)=0$
Factor each term.
$3x(x-2)+1(x-2)=0$
Factor out $(x-2)$.
$(x-2)(3x+1)=0$
Set each factor equal to zero.
$x-2=0$ or $3x+1=0$
Isolate $x$.
$x=2$ or $x=-\frac{1}{3}$
The solution set is $\{-\frac{1}{3},2\}$.
