Install RPM Fusion

sudo dnf install https://download1.rpmfusion.org/free/fedora/rpmfusion-free-release-$(rpm -E %fedora).noarch.rpm https://download1.rpmfusion.org/nonfree/fedora/rpmfusion-nonfree-release-$(rpm -E %fedora).noarch.rpm

Install packages

sudo dnf install -y kernel-devel-$(uname -r)
sudo dnf install -y akmodssudo dnf install -y broadcom-wl

Give the computer a reboot and the Broadcom card should now work.