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To solve the quadratic equation 2x^2 + 3x + 1 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 2, b = 3, and c = 1. Plugging these values into the formula, we get:

x = (-3 ± √(3^2 - 421)) / 2*2 x = (-3 ± √(9 - 8)) / 4 x = (-3 ± √1) / 4 x = (-3 ± 1) / 4

This gives us two possible solutions:

x1 = (-3 + 1) / 4 = -2 / 4 = -1/2 x2 = (-3 - 1) / 4 = -4 / 4 = -1

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