39a^2-18*22a+18*54=0

Solution for 39a^2-18*22a+18*54=0 equation:

39a^2-18*22a+18*54=0

We add all the numbers together, and all the variables

39a^2-18*22a+972=0

Wy multiply elements

39a^2-396a+972=0

a = 39; b = -396; c = +972;
Δ = b2-4ac
Δ = -3962-4·39·972
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-72}{2*39}=\frac{324}{78}
=4+2/13
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+72}{2*39}=\frac{468}{78}
=6
$