X+17=60/x

Solution for X+17=60/x equation:

X+17=60/X

We move all terms to the left:

X+17-(60/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-(+60/X)+17=0

We get rid of parentheses

X-60/X+17=0

We multiply all the terms by the denominator


X*X+17*X-60=0

We add all the numbers together, and all the variables

17X+X*X-60=0

Wy multiply elements

X^2+17X-60=0

a = 1; b = 17; c = -60;
Δ = b2-4ac
Δ = 172-4·1·(-60)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-23}{2*1}=\frac{-40}{2}
=-20
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+23}{2*1}=\frac{6}{2}
=3
$