22n^2-243n+11=0

Solution for 22n^2-243n+11=0 equation:

22n^2-243n+11=0

a = 22; b = -243; c = +11;
Δ = b2-4ac
Δ = -2432-4·22·11
Δ = 58081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{58081}=241$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-243)-241}{2*22}=\frac{2}{44}
=1/22
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-243)+241}{2*22}=\frac{484}{44}
=11
$