Solve the Quadratic Equation Featuring a Fraction: x² + 3x + 2.5 = 0

Solve the following equation:

$x^2+3x+2\frac{1}{2}=0$

To solve this problem, we'll apply the quadratic formula. The steps are as follows:

• Identify the coefficients: $a = 1$, $b = 3$, $c = 2.5$.
• Calculate the discriminant, $\Delta = b^2 - 4ac$.
• Apply the quadratic formula if the discriminant is non-negative.

Let's evaluate the discriminant:
Discriminant, $\Delta = b^2 - 4ac = 3^2 - 4 \cdot 1 \cdot 2.5 = 9 - 10 = -1$.

The discriminant is $-1$, which is less than zero. This means the quadratic equation has no real solutions. Complex solutions are not considered here based on the problem context.

Therefore, the solution to the problem is No solution.