X*(13-x)=26

Solution for X*(13-x)=26 equation:

X(13-X)=26

We move all terms to the left:

X(13-X)-(26)=0

We add all the numbers together, and all the variables

X(-1X+13)-26=0

We multiply parentheses

-1X^2+13X-26=0

a = -1; b = 13; c = -26;
Δ = b2-4ac
Δ = 132-4·(-1)·(-26)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{65}}{2*-1}=\frac{-13-\sqrt{65}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{65}}{2*-1}=\frac{-13+\sqrt{65}}{-2}
$