X-1=42/x

Solution for X-1=42/x equation:

X-1=42/X

We move all terms to the left:

X-1-(42/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-(+42/X)-1=0

We get rid of parentheses

X-42/X-1=0

We multiply all the terms by the denominator


X*X-1*X-42=0

We add all the numbers together, and all the variables

-1X+X*X-42=0

Wy multiply elements

X^2-1X-42=0

a = 1; b = -1; c = -42;
Δ = b2-4ac
Δ = -12-4·1·(-42)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-13}{2*1}=\frac{-12}{2}
=-6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+13}{2*1}=\frac{14}{2}
=7
$