x2-20x+100=9

Solution for x2-20x+100=9 equation:

x2-20x+100=9

We move all terms to the left:

x2-20x+100-(9)=0

We add all the numbers together, and all the variables

x^2-20x+91=0

a = 1; b = -20; c = +91;
Δ = b2-4ac
Δ = -202-4·1·91
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6}{2*1}=\frac{14}{2}
=7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6}{2*1}=\frac{26}{2}
=13
$