X(5-x)=-36

Solution for X(5-x)=-36 equation:

X(5-X)=-36

We move all terms to the left:

X(5-X)-(-36)=0

We add all the numbers together, and all the variables

X(-1X+5)-(-36)=0

We add all the numbers together, and all the variables

X(-1X+5)+36=0

We multiply parentheses

-1X^2+5X+36=0

a = -1; b = 5; c = +36;
Δ = b2-4ac
Δ = 52-4·(-1)·36
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-13}{2*-1}=\frac{-18}{-2}
=+9
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+13}{2*-1}=\frac{8}{-2}
=-4
$