X-1=7/x

Solution for X-1=7/x equation:

X-1=7/X

We move all terms to the left:

X-1-(7/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-(+7/X)-1=0

We get rid of parentheses

X-7/X-1=0

We multiply all the terms by the denominator


X*X-1*X-7=0

We add all the numbers together, and all the variables

-1X+X*X-7=0

Wy multiply elements

X^2-1X-7=0

a = 1; b = -1; c = -7;
Δ = b2-4ac
Δ = -12-4·1·(-7)
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{29}}{2*1}=\frac{1-\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{29}}{2*1}=\frac{1+\sqrt{29}}{2}
$