X+15=100/x

Solution for X+15=100/x equation:

X+15=100/X

We move all terms to the left:

X+15-(100/X)=0


Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

X-100/X+15=0

We multiply all the terms by the denominator


X*X+15*X-100=0

We add all the numbers together, and all the variables

15X+X*X-100=0

Wy multiply elements

X^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
$