s^2=5+s(1-8s)

Solution for s^2=5+s(1-8s) equation:

s^2=5+s(1-8s)

We move all terms to the left:

s^2-(5+s(1-8s))=0

We add all the numbers together, and all the variables

s^2-(5+s(-8s+1))=0


We calculate terms in parentheses: -(5+s(-8s+1)), so:

5+s(-8s+1)

determiningTheFunctionDomain
s(-8s+1)+5

We multiply parentheses

-8s^2+s+5

Back to the equation:

-(-8s^2+s+5)


We get rid of parentheses

s^2+8s^2-s-5=0

We add all the numbers together, and all the variables

9s^2-1s-5=0

a = 9; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·9·(-5)
Δ = 181
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{181}}{2*9}=\frac{1-\sqrt{181}}{18}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{181}}{2*9}=\frac{1+\sqrt{181}}{18}
$