X(x-2)=26

Solution for X(x-2)=26 equation:

X(X-2)=26

We move all terms to the left:

X(X-2)-(26)=0

We multiply parentheses

X^2-2X-26=0

a = 1; b = -2; c = -26;
Δ = b2-4ac
Δ = -22-4·1·(-26)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{3}}{2*1}=\frac{2-6\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{3}}{2*1}=\frac{2+6\sqrt{3}}{2}
$