w-1=-1/7w

Solution for w-1=-1/7w equation:

w-1=-1/7w

We move all terms to the left:

w-1-(-1/7w)=0


Domain of the equation: 7w)!=0

w!=0/1

w!=0

w∈R


We get rid of parentheses

w+1/7w-1=0

We multiply all the terms by the denominator


w*7w-1*7w+1=0

Wy multiply elements

7w^2-7w+1=0

a = 7; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·7·1
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{21}}{2*7}=\frac{7-\sqrt{21}}{14}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{21}}{2*7}=\frac{7+\sqrt{21}}{14}
$