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without solving the equation find the nature of the roots of quadratic equation √2x² -5√3+2√2​

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Find roots of the quadratic equation 2x²+3x+1=0 without calculating the discriminant

algebra-precalculus quadratics

Here is the equation I am stuck at:

2x2+3x+1=0

I need to find the roots without calculating the discriminant.

So this is where I stopped:

2x2+3x+1=0⇒x2+(3/2)x+1/2=0.

Everything is divided by 2 so I can get this form

x2−Sx+P=0; S=x1+x2 and P=x1x2

⇒S=x1+x2=−3/2, P=x1.x2=1/2.

How can I get the value of x1 and x2?