Answer
\begin{align*}
\text{Discriminant: }&
-116
\\\text{Number of Real Solutions: }&
0
\end{align*}
Work Step by Step
In the given equation,
\begin{align*}
6x^2-2x+5=0
,\end{align*} $a=
6
,$ $b=
-2
,$ and $c=
5
.$ Using the Discriminant Formula which is given by $b^2-4ac,$ the value of the discriminant is
\begin{array}{l}\require{cancel}
&
(-2)^2-4(6)(5)
\\&=
4-120
\\&=
-116
\end{array}
Since the discriminant is less than $0,$ then there is no real solution. Hence,
\begin{align*}
\text{Discriminant: }&
-116
\\\text{Number of Real Solutions: }&
0
\end{align*}
