X^2-22x-1=22

Solution for X^2-22x-1=22 equation:

X^2-22X-1=22

We move all terms to the left:

X^2-22X-1-(22)=0

We add all the numbers together, and all the variables

X^2-22X-23=0

a = 1; b = -22; c = -23;
Δ = b2-4ac
Δ = -222-4·1·(-23)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-24}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+24}{2*1}=\frac{46}{2}
=23
$