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.