This paper obtains a quasi-exactly solution to the Schrödinger equation. Its mathematical approach is based on a correspondence between quasi-exactly solvable models in quantum mechanics and sets of orthogonal polynomials. The quantum-mechanical wave function is the orthogonal polynomial in the energy. The condition of quasi-exact solvability is reflected in the vanishing of the norm of all polynomials. The zeros of the critical polynomial are the quasi-exact energy eigenvalues of the quantum mechanical systems.