x^2-9x+5=1

Solution for x^2-9x+5=1 equation:

x^2-9x+5=1

We move all terms to the left:

x^2-9x+5-(1)=0

We add all the numbers together, and all the variables

x^2-9x+4=0

a = 1; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·1·4
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{65}}{2*1}=\frac{9-\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{65}}{2*1}=\frac{9+\sqrt{65}}{2}
$