100/(x+15)=x

Solution for 100/(x+15)=x equation:

100/(x+15)=x

We move all terms to the left:

100/(x+15)-(x)=0


Domain of the equation: (x+15)!=0

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

x!=-15

x∈R


We add all the numbers together, and all the variables

-1x+100/(x+15)=0

We multiply all the terms by the denominator


-1x*(x+15)+100=0

We multiply parentheses

-x^2-15x+100=0

We add all the numbers together, and all the variables

-1x^2-15x+100=0

a = -1; b = -15; c = +100;
Δ = b2-4ac
Δ = -152-4·(-1)·100
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-25}{2*-1}=\frac{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+25}{2*-1}=\frac{40}{-2}
=-20
$