`2s^2+5s=3`

Divide throughout by 2.

`s^2+5/2s=3/2`

Take `1/2` of `5/2`, square it and add to both sides.

`s^2+5/2s+(5/4)^2=3/2+(5/4)^2`

Write the left side as a perfect square.

`(s+5/4)^2=3/2+25/16=(24+25)/16=49/16`

Solve for `s`.

`s+5/4=+-sqrt(49/16)`

`s=-5/4+-7/4=(-12)/4\ "or"\ 2/4`

`s=-3\ text(or)\ 1/2`