X(-x-9)-(8-x)=x

Solution for X(-x-9)-(8-x)=x equation:

X(-X-9)-(8-X)=X

We move all terms to the left:

X(-X-9)-(8-X)-(X)=0

We add all the numbers together, and all the variables

X(-1X-9)-(-1X+8)-X=0

We add all the numbers together, and all the variables

-1X+X(-1X-9)-(-1X+8)=0

We multiply parentheses

-1X^2-1X-9X-(-1X+8)=0

We get rid of parentheses

-1X^2-1X-9X+1X-8=0

We add all the numbers together, and all the variables

-1X^2-9X-8=0

a = -1; b = -9; c = -8;
Δ = b2-4ac
Δ = -92-4·(-1)·(-8)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7}{2*-1}=\frac{2}{-2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*-1}=\frac{16}{-2}
=-8
$