To solve the quadratic equation \( x^2 + 3x - 5 = 0 \), you can use the quadratic formula, which is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In your equation, \( a = 1 \), \( b = 3 \), and \( c = -5 \).
- Calculate the discriminant:
\[ b^2 - 4ac = 3^2 - 4 \cdot 1 \cdot (-5) = 9 + 20 = 29 \]
- Apply the quadratic formula:
\[ x = \frac{-3 \pm \sqrt{29}}{2 \cdot 1} = \frac{-3 \pm \sqrt{29}}{2} \]
So the solutions to the equation \( x^2 + 3x - 5 = 0 \) are:
\[ x = \frac{-3 + \sqrt{29}}{2} \quad \text{and} \quad x = \frac{-3 - \sqrt{29}}{2} \]