1/3s+2/3=4+2/6s

Solution for 1/3s+2/3=4+2/6s equation:

1/3s+2/3=4+2/6s

We move all terms to the left:

1/3s+2/3-(4+2/6s)=0


Domain of the equation: 3s!=0

s!=0/3

s!=0

s∈R



Domain of the equation: 6s)!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

1/3s-(2/6s+4)+2/3=0

We get rid of parentheses

1/3s-2/6s-4+2/3=0

We calculate fractions


6s/162s^2+(-54s)/162s^2+12s/162s^2-4=0

We multiply all the terms by the denominator


6s+(-54s)+12s-4*162s^2=0

We add all the numbers together, and all the variables

18s+(-54s)-4*162s^2=0

Wy multiply elements

-648s^2+18s+(-54s)=0

We get rid of parentheses

-648s^2+18s-54s=0

We add all the numbers together, and all the variables

-648s^2-36s=0

a = -648; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-648)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*-648}=\frac{0}{-1296}
=0
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-648}=\frac{72}{-1296}
=-1/18
$