x^2-26x+169=25

Solution for x^2-26x+169=25 equation:

x^2-26x+169=25

We move all terms to the left:

x^2-26x+169-(25)=0

We add all the numbers together, and all the variables

x^2-26x+144=0

a = 1; b = -26; c = +144;
Δ = b2-4ac
Δ = -262-4·1·144
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-10}{2*1}=\frac{16}{2}
=8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+10}{2*1}=\frac{36}{2}
=18
$