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!=0

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*x+100=0

We add all the numbers together, and all the variables

15x-1x*x+100=0

Wy multiply elements

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