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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-9x-8=0

a = 1; b = -9; c = -8;
Δ = b2-4ac
Δ = -92-4·1·(-8)
Δ = 113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{113}}{2*1}=\frac{9-\sqrt{113}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{113}}{2*1}=\frac{9+\sqrt{113}}{2}
$