To solve the quadratic equation 2x² + 5x + 3 = 0, we can use the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / (2a)
In our equation, the coefficients are:
- a = 2
- b = 5
- c = 3
Now, we can plug these values into the formula:
First, calculate the discriminant, b² – 4ac:
- b² = 5² = 25
- 4ac = 4 * 2 * 3 = 24
- Discriminant = 25 – 24 = 1
Since the discriminant is positive, this means there are two distinct real solutions. Next, we can substitute back into the quadratic formula:
x = (-5 ± √1) / (2 * 2)
Calculating the two possible values for x:
- x₁ = (-5 + 1) / 4 = -4 / 4 = -1
- x₂ = (-5 – 1) / 4 = -6 / 4 = -3/2
Therefore, the solutions to the equation 2x² + 5x + 3 = 0 are:
- x = -1
- x = -1.5