x2-22x+121=90

Solution for x2-22x+121=90 equation:

x2-22x+121=90

We move all terms to the left:

x2-22x+121-(90)=0

We add all the numbers together, and all the variables

x^2-22x+31=0

a = 1; b = -22; c = +31;
Δ = b2-4ac
Δ = -222-4·1·31
Δ = 360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-6\sqrt{10}}{2*1}=\frac{22-6\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+6\sqrt{10}}{2*1}=\frac{22+6\sqrt{10}}{2}
$