n^2-22n=121

Solution for n^2-22n=121 equation:

n^2-22n=121

We move all terms to the left:

n^2-22n-(121)=0

a = 1; b = -22; c = -121;
Δ = b2-4ac
Δ = -222-4·1·(-121)
Δ = 968
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{968}=\sqrt{484*2}=\sqrt{484}*\sqrt{2}=22\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22\sqrt{2}}{2*1}=\frac{22-22\sqrt{2}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22\sqrt{2}}{2*1}=\frac{22+22\sqrt{2}}{2}
$