S(t)=2t/t-1

Solution for S(t)=2t/t-1 equation:

(S)=2S/S-1

We move all terms to the left:

(S)-(2S/S-1)=0


Domain of the equation: S-1)!=0

S∈R


We get rid of parentheses

S-2S/S+1=0

We multiply all the terms by the denominator


S*S-2S+1*S=0

We add all the numbers together, and all the variables

-1S+S*S=0

Wy multiply elements

S^2-1S=0

a = 1; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·1·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*1}=\frac{0}{2}
=0
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*1}=\frac{2}{2}
=1
$