s^2=4+s(1-6s)

Solution for s^2=4+s(1-6s) equation:

s^2=4+s(1-6s)

We move all terms to the left:

s^2-(4+s(1-6s))=0

We add all the numbers together, and all the variables

s^2-(4+s(-6s+1))=0


We calculate terms in parentheses: -(4+s(-6s+1)), so:

4+s(-6s+1)

determiningTheFunctionDomain
s(-6s+1)+4

We multiply parentheses

-6s^2+s+4

Back to the equation:

-(-6s^2+s+4)


We get rid of parentheses

s^2+6s^2-s-4=0

We add all the numbers together, and all the variables

7s^2-1s-4=0

a = 7; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·7·(-4)
Δ = 113
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{113}}{2*7}=\frac{1-\sqrt{113}}{14}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{113}}{2*7}=\frac{1+\sqrt{113}}{14}
$