16/(x+17)=x

Solution for 16/(x+17)=x equation:

16/(x+17)=x

We move all terms to the left:

16/(x+17)-(x)=0


Domain of the equation: (x+17)!=0

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

x!=-17

x∈R


We add all the numbers together, and all the variables

-1x+16/(x+17)=0

We multiply all the terms by the denominator


-1x*(x+17)+16=0

We multiply parentheses

-x^2-17x+16=0

We add all the numbers together, and all the variables

-1x^2-17x+16=0

a = -1; b = -17; c = +16;
Δ = b2-4ac
Δ = -172-4·(-1)·16
Δ = 353
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{-(-17)-\sqrt{353}}{2*-1}=\frac{17-\sqrt{353}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{353}}{2*-1}=\frac{17+\sqrt{353}}{-2}
$