X(26-x)=26

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

X(26-X)=26

We move all terms to the left:

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

We add all the numbers together, and all the variables

X(-1X+26)-26=0

We multiply parentheses

-1X^2+26X-26=0

a = -1; b = 26; c = -26;
Δ = b2-4ac
Δ = 262-4·(-1)·(-26)
Δ = 572
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:

$\sqrt{\Delta}=\sqrt{572}=\sqrt{4*143}=\sqrt{4}*\sqrt{143}=2\sqrt{143}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{143}}{2*-1}=\frac{-26-2\sqrt{143}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{143}}{2*-1}=\frac{-26+2\sqrt{143}}{-2}
$