20z^2-156z+216=0

Solution for 20z^2-156z+216=0 equation:

20z^2-156z+216=0

a = 20; b = -156; c = +216;
Δ = b2-4ac
Δ = -1562-4·20·216
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-84}{2*20}=\frac{72}{40}
=1+4/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+84}{2*20}=\frac{240}{40}
=6
$