x(13-x)=42

Solution for x(13-x)=42 equation:

x(13-x)=42

We move all terms to the left:

x(13-x)-(42)=0

We add all the numbers together, and all the variables

x(-1x+13)-42=0

We multiply parentheses

-1x^2+13x-42=0

a = -1; b = 13; c = -42;
Δ = b2-4ac
Δ = 132-4·(-1)·(-42)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-1}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+1}{2*-1}=\frac{-12}{-2}
=+6
$