Diophantine Equation

from math import sqrt

def sol_equa(n):
    LIMIT = 1000
    solutions = list()
    for y in range(1, LIMIT):
        for x in range(y, LIMIT):
            if x**2 - 4 * y**2 == n:
                solutions.append([x, y])
    return solutions


def sol_equa2(n):
    solutions = list()
    for y in range(1, 50000):
        x_squared = 4 * y**2 + n
        if sqrt(x_squared) == int(sqrt(x_squared)):
            solutions.append([int(sqrt(x_squared)), y])
    return solutions


# MAIN FUNCTION
print(sol_equa(5))
print(sol_equa(21))
print(sol_equa2(90005))