27z^2-21z+2=0

Solution for 27z^2-21z+2=0 equation:

27z^2-21z+2=0

a = 27; b = -21; c = +2;
Δ = b2-4ac
Δ = -212-4·27·2
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-15}{2*27}=\frac{6}{54}
=1/9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+15}{2*27}=\frac{36}{54}
=2/3
$