The acute angle between two lines can be found using the formula: \(\tan{\theta} = \left|\frac{m_1 - m_2}{1 + m_1m_2}\right|\) where \(m_1\) and \(m_2\) are the slopes of the two lines.

The slope-intercept form of a line is given by the equation: \(y = mx + b\), where \(m\) is the slope of the line and \(b\) is the y-intercept.

The given lines are: 2x + y = 3 and 3x - 2y = 5. We can rewrite these equations in slope-intercept form to find their slopes:

y = -2x + 3, so the slope of the first line is \(m_1 = -2\).

-2y = -3x + 5, so y = (3/2)x - (5/2), and the slope of the second line is \(m_2 = 3/2\).

Substituting these values into the formula for the tangent of the acute angle between two lines, we get:

\(\tan{\theta} = \left|\frac{-2 - \frac{3}{2}}{1 + (-2)\left(\frac{3}{2}\right)}\right|\)

Simplifying this expression, we get:

\(\tan{\theta} = \left|\frac{-\frac{7}{2}}{1 - 3}\right|\)

\(\tan{\theta} = \left|\frac{-\frac{7}{2}}{-2}\right|\)

\(\tan{\theta} = \frac{7}{4}\)

So, the tangent of the acute angle between the lines 2x + y = 3 and 3x - 2y = 5 is 7/4.