(a^2)-3a-22=1

Solution for (a^2)-3a-22=1 equation:

(a^2)-3a-22=1

We move all terms to the left:

(a^2)-3a-22-(1)=0

We add all the numbers together, and all the variables

a^2-3a-23=0

a = 1; b = -3; c = -23;
Δ = b2-4ac
Δ = -32-4·1·(-23)
Δ = 101
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{101}}{2*1}=\frac{3-\sqrt{101}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{101}}{2*1}=\frac{3+\sqrt{101}}{2}
$