w2-26w=-1

Solution for w2-26w=-1 equation:

w2-26w=-1

We move all terms to the left:

w2-26w-(-1)=0

We add all the numbers together, and all the variables

w^2-26w+1=0

a = 1; b = -26; c = +1;
Δ = b2-4ac
Δ = -262-4·1·1
Δ = 672
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-4\sqrt{42}}{2*1}=\frac{26-4\sqrt{42}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+4\sqrt{42}}{2*1}=\frac{26+4\sqrt{42}}{2}
$