s=2+1/3s

Solution for s=2+1/3s equation:

s=2+1/3s

We move all terms to the left:

s-(2+1/3s)=0


Domain of the equation: 3s)!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

s-(1/3s+2)=0

We get rid of parentheses

s-1/3s-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

3s^2-6s-1=0

a = 3; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·3·(-1)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{3}}{2*3}=\frac{6-4\sqrt{3}}{6}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{3}}{2*3}=\frac{6+4\sqrt{3}}{6}
$