use the quadratic formula to solve the equation.

2x^2 + 5x +3 = 0

The quadratic formula is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

In this case, a = 2, b = 5, and c = 3. Substituting these values into the formula, we get:

x = (-5 ± sqrt(5^2 - 4(2)(3))) / 2(2)

x = (-5 ± sqrt(25 - 24)) / 4

x = (-5 ± 1) / 4

So the solutions are:

x = (-5 + 1) / 4 = -1

x = (-5 - 1) / 4 = -3/2

Therefore, the solutions to the equation 2x^2 + 5x + 3 = 0 are x = -1 and x = -3/2.