Since every Non deterministic Turing machine has an equivalent deterministic Turing machine. Why we can not solve NP problem using the deterministic TM?
In the second construction, the constructed DTM effectively performs a breadth-first search of the NTM's computation tree, visiting all possible computations of the NTM in order of increasing length until it finds an accepting one. Therefore, the length of an accepting computation of the DTM is, in general, exponential in the length of the shortest accepting computation of the NTM. This is believed to be a general property of simulations of NTMs by DTMs. The P = NP problem, the most famous unresolved question in computer science, concerns one case of this issue: whether or not every problem solvable by a NTM in polynomial time is necessarily also solvable by a DTM in polynomial time.
To paraphrase, when you convert the NTM to the corresponding DTM, your solution's algorithmic complexity will become exponential for NP problems.
If you can prove that is not the case (for any NP problem), congratulations, you've proven that P=NP.