The given expression is a quadratic equation in the form \( ax^2 + bx + c = 0 \), where \( a = 1 \), \( b = 3m \), and \( c = m \).
To solve for \( x \), you can use the quadratic formula:
\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \]
Substituting the values of \( a \), \( b \), and \( c \):
\[ x = \frac{{-3m \pm \sqrt{{(3m)^2 - 4(1)(m)}}}}{{2(1)}} \] \[ x = \frac{{-3m \pm \sqrt{{9m^2 - 4m}}}}{2} \] \[ x = \frac{{-3m \pm \sqrt{{m(9m - 4)}}}}{2} \]
This provides the solutions for \( x \) in terms of \( m \) as follows:
\[ x = \frac{{-3m + \sqrt{{m(9m - 4)}}}}{2} \quad \text{and} \quad x = \frac{{-3m - \sqrt{{m(9m - 4)}}}}{2} \]
You can simplify further if necessary or evaluate at specific values of \( m \) as needed.