x(13-X)=5

Solution for x(13-X)=5 equation:

x(13-x)=5

We move all terms to the left:

x(13-x)-(5)=0

We add all the numbers together, and all the variables

x(-1x+13)-5=0

We multiply parentheses

-1x^2+13x-5=0

a = -1; b = 13; c = -5;
Δ = b2-4ac
Δ = 132-4·(-1)·(-5)
Δ = 149
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{149}}{2*-1}=\frac{-13-\sqrt{149}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{149}}{2*-1}=\frac{-13+\sqrt{149}}{-2}
$