105/(x-8)=x

Solution for 105/(x-8)=x equation:

105/(x-8)=x

We move all terms to the left:

105/(x-8)-(x)=0


Domain of the equation: (x-8)!=0

We move all terms containing x to the left, all other terms to the right

x!=8

x∈R


We add all the numbers together, and all the variables

-1x+105/(x-8)=0

We multiply all the terms by the denominator


-1x*(x-8)+105=0

We multiply parentheses

-x^2+8x+105=0

We add all the numbers together, and all the variables

-1x^2+8x+105=0

a = -1; b = 8; c = +105;
Δ = b2-4ac
Δ = 82-4·(-1)·105
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-22}{2*-1}=\frac{-30}{-2}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+22}{2*-1}=\frac{14}{-2}
=-7
$