x(-13-x)=22

Solution for x(-13-x)=22 equation:

x(-13-x)=22

We move all terms to the left:

x(-13-x)-(22)=0

We add all the numbers together, and all the variables

x(-1x-13)-22=0

We multiply parentheses

-1x^2-13x-22=0

a = -1; b = -13; c = -22;
Δ = b2-4ac
Δ = -132-4·(-1)·(-22)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-9}{2*-1}=\frac{4}{-2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+9}{2*-1}=\frac{22}{-2}
=-11
$