2z^2+3z+1=3

Solution for 2z^2+3z+1=3 equation:

2z^2+3z+1=3

We move all terms to the left:

2z^2+3z+1-(3)=0

We add all the numbers together, and all the variables

2z^2+3z-2=0

a = 2; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·2·(-2)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5}{2*2}=\frac{-8}{4}
=-2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5}{2*2}=\frac{2}{4}
=1/2
$