# Intersection point for existing solution - avoiding error messages, message in diagram if no solution exists

I am trying to highlight the intersection if one exists. For specific parameter values there is no solution and the manipulate output creates error message and red background.

How can I avoid the messages with a conditional statement - highlight the point or drop the point (potentially a message in the legend that intersection does not exist).

Clear["Global*"]
f[a_, x_] := a + x^2;
g[b_, x_] := b + x;

intersect[a_, b_] := {x, f[a, x]} /.
Solve[{f[a, x] == g[b, x], a >= 0, b >= 0, x >= 0}, x][[1]]

Manipulate[
Plot[Evaluate@{f[a, x], g[b, x]}, {x, 0, 50},
PlotLegends -> Placed["Expressions", {0.7, 0.7}],
PlotRange -> {-25, 500},
Epilog -> {Red, Point@intersect[a, b] }],
{{a, 50}, 0, 100, 1, Appearance -> "Labeled"}, {{b, 75}, -10, 100, 1, Appearance -> "Labeled"},
Button["Reset", {a = 50, b = 75}, ImageSize -> Medium]]


Thank you!

Clear["Global*"]
f[a_, x_] := a + x^2;
g[b_, x_] := b + x;

intersect[a_, b_] := Module[
{sol = Solve[{f[a, x] == g[b, x], a >= 0, b >= 0, x >= 0}, x]},
If[sol === {}, {}, {x, f[a, x]} /. sol[[1]]]]

Manipulate[Plot[Evaluate@{f[a, x], g[b, x]}, {x, 0, 50},
PlotLegends -> {Placed["Expressions", {0.7, 0.7}],
Placed[PointLegend[{Red},
If[intersect[a, b] === {}, {"no intersection"},
{N@intersect[a, b]}]], {0.7, 0.5}]},
PlotRange -> {-25, 500},
Epilog -> {Red, Point@intersect[a, b]}],
{{a, 50}, 0, 100, 1, Appearance -> "Labeled"},
{{b, 75}, -10, 100, 1, Appearance -> "Labeled"},
Button["Reset", {a = 50, b = 75}, ImageSize -> Medium]]