s=1/8s+1

Solution for s=1/8s+1 equation:

s=1/8s+1

We move all terms to the left:

s-(1/8s+1)=0


Domain of the equation: 8s+1)!=0

s∈R


We get rid of parentheses

s-1/8s-1=0

We multiply all the terms by the denominator


s*8s-1*8s-1=0

Wy multiply elements

8s^2-8s-1=0

a = 8; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·8·(-1)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{6}}{2*8}=\frac{8-4\sqrt{6}}{16}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{6}}{2*8}=\frac{8+4\sqrt{6}}{16}
$