The equation $2x^2+3x+1=0$ has

$2x^2+3x+1=0$

Where $a=2,b=3,c=1$

$\Delta =b^2-4ac=3^2-4\left(2\right)\left(1\right)$

$\Delta =9-8=1$  is perfect square so $2x^2+3x+1=0$  has no irrational roots