Solve \( 4 w(w+3)+15=0 \) by using the quadratic formula. If there is no solution, enter \( \varnothing \). Provide your answer below.

To solve the equation \( 4w(w+3)+15=0 \), we first expand and rearrange it: \[ 4w^2 + 12w + 15 = 0. \] Now we can identify the coefficients for the quadratic formula, which is \( w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a = 4 \), \( b = 12 \), and \( c = 15 \). 1. **Calculate the discriminant**: \[ b^2 - 4ac = 12^2 - 4 \cdot 4 \cdot 15 = 144 - 240 = -96. \] Since the discriminant is negative, this indicates that there are no real solutions. Thus, the final answer is: \[ \varnothing. \]