x^2-x-22=9

Solution for x^2-x-22=9 equation:

x^2-x-22=9

We move all terms to the left:

x^2-x-22-(9)=0

We add all the numbers together, and all the variables

x^2-1x-31=0

a = 1; b = -1; c = -31;
Δ = b2-4ac
Δ = -12-4·1·(-31)
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{5}}{2*1}=\frac{1-5\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{5}}{2*1}=\frac{1+5\sqrt{5}}{2}
$