Answer
$\text{Discriminant: }
164
\\\text{Number of real solutions: }
2$
Work Step by Step
Using the properties of equality, the given equation, $
4x^2-2x=10
,$ is equivalent to
\begin{align*}
4x^2-2x-10&=10-10
\\
4x^2-2x-10&=0
.\end{align*}
Using $ax^2+bx+c=0,$ the equation above has $a=
4
,$ $b=
-2
,$ and $c=
-10
.$ Using $b^2-4ac$ or the Discriminant, then
\begin{align*}b^2-4ac&=
(-2)^2-4(4)(-10)
\\&=
4+160
\\&=
164
.\end{align*}
Since the discriminant above is greater than $0,$ then there are $2$ real solutions. Hence,
\begin{align*}
\text{Discriminant: }
164
\\\text{Number of real solutions: }
2
.\end{align*}
