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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


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

8+s(-8s+5)

determiningTheFunctionDomain
s(-8s+5)+8

We multiply parentheses

-8s^2+5s+8

Back to the equation:

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


We get rid of parentheses

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

We add all the numbers together, and all the variables

9s^2-5s-8=0

a = 9; b = -5; c = -8;
Δ = b2-4ac
Δ = -52-4·9·(-8)
Δ = 313
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{-(-5)-\sqrt{313}}{2*9}=\frac{5-\sqrt{313}}{18}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{313}}{2*9}=\frac{5+\sqrt{313}}{18}
$