Bending Strength Calculation for St3s Steel I-Beam 120: 4m Span, 2.3 Tonne Load & Maximum Moment

Hello,
I have such a problem. I have an I-beam 120 from St3s steel which I want to mount on two supports spaced 4m apart. It loads the beam with a constant load of 2.3 tonnes.
I count the maximum bending moment according to the formula: gl ^ 2/8 and it goes out 46000Nm
Wx for this I-beam is 0.0000547 m ^ 3
So I'm counting Mgmax / Wx and some 840Mpa comes out. Max for St3s steel is around 145Mpa.

My question is: do I count it right? I don't want to believe in such a result.
Regards !

EDIT

I check the units and I think I know where I made the mistake: for q I should take 5750N / m, right?

You haven't distributed the load (q = P / l) - something around 206 MPa comes out. And so exceeded, but not eight times .

Thanks for the help !

From what I am counting now, I-140 is also not a good idea because the bending stress max is around 140MPa.

Then I take 160.