Evaluate the following formula for the values given. \[ x=\frac{-b+\sqrt{b^{2}-4 a c}}{2 a} \text { when } a=2, b=-5, \text { and } c=-3 \text {. } \] \( x=\square \)

Let's plug in the values into the formula: 1. First, calculate \( b^2 - 4ac \): \[ b^2 = (-5)^2 = 25 \] \[ 4ac = 4 \cdot 2 \cdot (-3) = -24 \] \[ b^2 - 4ac = 25 - (-24) = 25 + 24 = 49 \] 2. Now, calculate \( \sqrt{b^2 - 4ac} \): \[ \sqrt{49} = 7 \] 3. Substitute \( a \), \( b \), and the square root back into the formula for \( x \): \[ x = \frac{-(-5) + 7}{2 \cdot 2} = \frac{5 + 7}{4} = \frac{12}{4} = 3 \] So, the value of \( x \) is \( \boxed{3} \).