X(4-k)=9,k

Solution for X(4-k)=9,k equation:

X(4-X)=9.X

We move all terms to the left:

X(4-X)-(9.X)=0

We add all the numbers together, and all the variables

X(-1X+4)-(+9.X)=0

We multiply parentheses

-1X^2+4X-(+9.X)=0

We get rid of parentheses

-1X^2+4X-9.X=0

We add all the numbers together, and all the variables

-1X^2-5X=0

a = -1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-1)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-1}=\frac{0}{-2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-1}=\frac{10}{-2}
=-5
$