27a^2-57a+20=0

Solution for 27a^2-57a+20=0 equation:

27a^2-57a+20=0

a = 27; b = -57; c = +20;
Δ = b2-4ac
Δ = -572-4·27·20
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-33}{2*27}=\frac{24}{54}
=4/9
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+33}{2*27}=\frac{90}{54}
=1+2/3
$