There's no virtualization software that can run x86_64 guests without VT-x because because isolation of the virtual machine would be impossible without it1.
However, there are a few solutions for you
This may provide even better performance than hardware-assisted virtualization because of the low overhead, but it needs a modified kernel so it'll only work if you use Linux guests (or other OSes with open-source and patchable kernels).
If that's your case then you can use Xen which can run 64-bit guests without needing VT-x
Emulator softwares can run any guest architectures under any hosts. So you need an x86_64 emulator like qemu or Bochs. But be aware that it'll be much slower than other solutions
The initial version of x86-64 (AMD64) did not allow for a software-only full virtualization due to the lack of segmentation support in long mode, which made the protection of the hypervisor's memory impossible, in particular, the protection of the trap handler that runs in the guest kernel address space.
Revision D and later 64-bit AMD processors (as a rule of thumb, those manufactured in 90 nm or less) added basic support for segmentation in long mode, making it possible to run 64-bit guests in 64-bit hosts via binary translation. Intel did not add segmentation support to its x86-64 implementation (Intel 64), making 64-bit software-only virtualization impossible on Intel CPUs, but Intel VT-x support makes 64-bit hardware assisted virtualization possible on the Intel platform