-1/w+1=-9w-6

Solution for -1/w+1=-9w-6 equation:

-1/w+1=-9w-6

We move all terms to the left:

-1/w+1-(-9w-6)=0


Domain of the equation: w!=0

w∈R


We get rid of parentheses

-1/w+9w+6+1=0

We multiply all the terms by the denominator


9w*w+6*w+1*w-1=0

We add all the numbers together, and all the variables

7w+9w*w-1=0

Wy multiply elements

9w^2+7w-1=0

a = 9; b = 7; c = -1;
Δ = b2-4ac
Δ = 72-4·9·(-1)
Δ = 85
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{85}}{2*9}=\frac{-7-\sqrt{85}}{18}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{85}}{2*9}=\frac{-7+\sqrt{85}}{18}
$