diff --git a/modules/core/src/mathfuncs.cpp b/modules/core/src/mathfuncs.cpp
index 7af66c5723..90713fb27d 100644
--- a/modules/core/src/mathfuncs.cpp
+++ b/modules/core/src/mathfuncs.cpp
@@ -1631,9 +1631,16 @@ int cv::solveCubic( InputArray _coeffs, OutputArray _roots )
         a3 *= a0;
 
         double Q = (a1 * a1 - 3 * a2) * (1./9);
-        double R = (2 * a1 * a1 * a1 - 9 * a1 * a2 + 27 * a3) * (1./54);
+        double R = (a1 * (2 * a1 * a1 - 9 * a2) + 27 * a3) * (1./54);
         double Qcubed = Q * Q * Q;
-        double d = Qcubed - R * R;
+        /*
+          Here we expand expression `Qcubed - R * R` for `d` variable
+          to reduce common terms `a1^6 / 729` and `-a1^4 * a2 / 81`
+          and thus decrease rounding error (in case of quite big coefficients).
+
+          And then we additionally group terms to further reduce rounding error.
+        */
+        double d = (a1 * a1 * (a2 * a2 - 4 * a1 * a3) + 2 * a2 * (9 * a1 * a3 - 2 * a2 * a2) - 27 * a3 * a3) * (1./108);
 
         if( d > 0 )
         {
diff --git a/modules/core/test/test_math.cpp b/modules/core/test/test_math.cpp
index 6ff4d4984d..c6686cf1c4 100644
--- a/modules/core/test/test_math.cpp
+++ b/modules/core/test/test_math.cpp
@@ -2522,7 +2522,7 @@ TEST(Core_SolveCubicCubic, accuracy)
         const auto num_roots = solveCubic(coeffs, roots);
 
         EXPECT_EQ(num_roots, 1);
-        EXPECT_EQ(roots[0], 1.);
+        EXPECT_NEAR(roots[0], 1., 1e-8);
     }
 
     {
@@ -2568,7 +2568,7 @@ TEST(Core_SolveCubicNormalizedCubic, accuracy)
         const auto num_roots = solveCubic(coeffs, roots);
 
         EXPECT_EQ(num_roots, 1);
-        EXPECT_EQ(roots[0], 1.);
+        EXPECT_NEAR(roots[0], 1., 1e-8);
     }
 
     {
@@ -2597,6 +2597,27 @@ TEST(Core_SolveCubicNormalizedCubic, accuracy)
     }
 }
 
+TEST(Core_SolveCubic, regression_27323)
+{
+    {
+        const std::vector<double> coeffs{2e-13, 1, -2, 1};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_EQ(num_roots, 1);
+        EXPECT_EQ(roots[0], -5e12 - 2.);
+    }
+
+    {
+        const std::vector<double> coeffs{5e12, -1e13, 5e12};
+        std::vector<double> roots;
+        const auto num_roots = solveCubic(coeffs, roots);
+
+        EXPECT_EQ(num_roots, 1);
+        EXPECT_EQ(roots[0], -5e12 - 2.);
+    }
+}
+
 TEST(Core_SolvePoly, regression_5599)
 {
     // x^4 - x^2 = 0, roots: 1, -1, 0, 0