3+2z=21z2

Solution for 3+2z=21z2 equation:

3+2z=21z^2

We move all terms to the left:

3+2z-(21z^2)=0

determiningTheFunctionDomain
-21z^2+2z+3=0

a = -21; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-21)·3
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-16}{2*-21}=\frac{-18}{-42}
=3/7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+16}{2*-21}=\frac{14}{-42}
=-1/3
$