169m^2-26m+1=(1+13)^2

Solution for 169m^2-26m+1=(1+13)^2 equation:

169m^2-26m+1=(1+13)^2

We move all terms to the left:

169m^2-26m+1-((1+13)^2)=0

We add all the numbers together, and all the variables

169m^2-26m+1-(14^2)=0

We add all the numbers together, and all the variables

169m^2-26m-195=0

a = 169; b = -26; c = -195;
Δ = b2-4ac
Δ = -262-4·169·(-195)
Δ = 132496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{132496}=364$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-364}{2*169}=\frac{-338}{338}
=-1
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+364}{2*169}=\frac{390}{338}
=1+2/13
$