X+5=84/x

Solution for X+5=84/x equation:

X+5=84/X

We move all terms to the left:

X+5-(84/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-(+84/X)+5=0

We get rid of parentheses

X-84/X+5=0

We multiply all the terms by the denominator


X*X+5*X-84=0

We add all the numbers together, and all the variables

5X+X*X-84=0

Wy multiply elements

X^2+5X-84=0

a = 1; b = 5; c = -84;
Δ = b2-4ac
Δ = 52-4·1·(-84)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*1}=\frac{-24}{2}
=-12
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*1}=\frac{14}{2}
=7
$