x=x2-10x+1

Solution for x=x2-10x+1 equation:

x=x2-10x+1

We move all terms to the left:

x-(x2-10x+1)=0

We add all the numbers together, and all the variables

-(+x^2-10x+1)+x=0

We get rid of parentheses

-x^2+10x+x-1=0

We add all the numbers together, and all the variables

-1x^2+11x-1=0

a = -1; b = 11; c = -1;
Δ = b2-4ac
Δ = 112-4·(-1)·(-1)
Δ = 117
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:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3\sqrt{13}}{2*-1}=\frac{-11-3\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3\sqrt{13}}{2*-1}=\frac{-11+3\sqrt{13}}{-2}
$