closes sympy#22058

Since Poly can handle symbolic coefficients, it is not necessary
to remove powers in them with unrad: passing the variable of
interest will allow a lower order polynomial to be solved.
e.g. unrad(sqrt(t)*x, x) is unchanged while unrad(sqrt(t)*x) is t*x**2

Also, only explicitly check solutions of FiniteSet.

sympy/solvers/solveset.py

@@ -862,7 +862,7 @@ def _solve_radical(f, unradf, symbol, solveset_solver):
         result = Union(*[imageset(Lambda(y, g_y), f_y_sols)
                          for g_y in g_y_s])
 
-    if isinstance(result, (Complement, ConditionSet)):
+    if not isinstance(result, FiniteSet):
         solution_set = result
     else:
         f_set = []  # solutions for FiniteSet
@@ -1067,7 +1067,7 @@ def _solveset(f, symbol, domain, _check=False):
         elif isinstance(rhs_s, FiniteSet):
             for equation in [lhs - rhs for rhs in rhs_s]:
                 if equation == f:
-                    u = unrad(f)
+                    u = unrad(f, symbol)
                     if u:
                         result += _solve_radical(equation, u,
                                                  symbol,
@@ -3448,7 +3448,7 @@ def _separate_poly_nonpoly(system, symbols):
         if isinstance(eq, Equality):
             eq = eq.rewrite(Add)
         # try to remove sqrt and rational power
-        without_radicals = unrad(simplify(eq))
+        without_radicals = unrad(simplify(eq), *symbols)
         if without_radicals:
             eq_unrad, cov = without_radicals
             if not cov:

sympy/solvers/tests/test_solveset.py

@@ -3064,3 +3064,9 @@ def test_issue_19144():
 def test_issue_19814():
     assert nonlinsolve([ 2**m - 2**(2*n), 4*2**m - 2**(4*n)], m, n
                       ) == FiniteSet((log(2**(2*n))/log(2), S.Complexes))
+
+
+def test_issue_22058():
+    sol = solveset(-sqrt(t)*x**2 + 2*x + sqrt(t), x, S.Reals)
+    # doesn't fail (and following numerical check)
+    assert sol.xreplace({t: 1}) == {1 - sqrt(2), 1 + sqrt(2)}, sol.xreplace({t: 1})