3s^-1/3s^-1=1

Solution for 3s^-1/3s^-1=1 equation:

3s^-1/3s^-1=1

We move all terms to the left:

3s^-1/3s^-1-(1)=0


Domain of the equation: 3s^!=0

s!=0/3

s!=0

s∈R


We add all the numbers together, and all the variables

3s-1/3s^-2=0

We multiply all the terms by the denominator


3s*3s^-2*3s^-1=0

Wy multiply elements

9s^2-6s-1=0

a = 9; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·9·(-1)
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{2}}{2*9}=\frac{6-6\sqrt{2}}{18}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{2}}{2*9}=\frac{6+6\sqrt{2}}{18}
$