Answer
two real solutions
Work Step by Step
Using the properties of equality, the given quadratic equation, $
3x^2=5-7x
,$ is equivalent to
\begin{array}{l}\require{cancel}
3x^2+7x-5=0
.\end{array}
The quadratic equation above has the following coefficients:
\begin{array}{l}\require{cancel}
a=
3
\\b=
7
\\c=
-5
.\end{array}
Substituting these values into $b^2-4ac$ (or the Discriminant), then the value of the discriminant is
\begin{array}{l}\require{cancel}
(7)^2-4(3)(-5)
\\\\=
49+60
\\\\=
109
.\end{array}
Since the value of the discriminant is $\text{
greater than zero
,}$ then the given quadratic equation has $\text{
two real solutions
}$.