Answer
$\text{Discriminant: }
0
\\\text{Number of real solutions: }
1$
Work Step by Step
Using the properties of equality, the given equation, $
3x^2+3=6x
,$ is equivalent to
\begin{align*}
3x^2-6x+3=0
.\end{align*}
Using $ax^2+bx+c=0,$ the equation above has $a=
3
,$ $b=
-6
,$ and $c=
3
.$ Using $b^2-4ac$ or the Discriminant, then
\begin{align*}b^2-4ac&=
(-6)^2-4(3)(3)
\\&=
36-36
\\&=
0
.\end{align*}
Since the discriminant above is equal to $0,$ then there is $1$ real solutions. Hence,
\begin{align*}
\text{Discriminant: }
0
\\\text{Number of real solutions: }
1
.\end{align*}
