a^2-22a-1=0

Solution for a^2-22a-1=0 equation:

a^2-22a-1=0

a = 1; b = -22; c = -1;
Δ = b2-4ac
Δ = -222-4·1·(-1)
Δ = 488
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{488}=\sqrt{4*122}=\sqrt{4}*\sqrt{122}=2\sqrt{122}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{122}}{2*1}=\frac{22-2\sqrt{122}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{122}}{2*1}=\frac{22+2\sqrt{122}}{2}
$