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

Solution for 3s^-1/3s^-1=0 equation:

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

We multiply all the terms by the denominator


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

Wy multiply elements

9s^2-3s-1=0

a = 9; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·9·(-1)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{5}}{2*9}=\frac{3-3\sqrt{5}}{18}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{5}}{2*9}=\frac{3+3\sqrt{5}}{18}
$