5-11/3s=5/6s+4

Solution for 5-11/3s=5/6s+4 equation:

5-11/3s=5/6s+4

We move all terms to the left:

5-11/3s-(5/6s+4)=0


Domain of the equation: 3s!=0

s!=0/3

s!=0

s∈R



Domain of the equation: 6s+4)!=0

s∈R


We get rid of parentheses

-11/3s-5/6s-4+5=0

We calculate fractions


(-66s)/18s^2+(-15s)/18s^2-4+5=0

We add all the numbers together, and all the variables

(-66s)/18s^2+(-15s)/18s^2+1=0

We multiply all the terms by the denominator


(-66s)+(-15s)+1*18s^2=0

Wy multiply elements

18s^2+(-66s)+(-15s)=0

We get rid of parentheses

18s^2-66s-15s=0

We add all the numbers together, and all the variables

18s^2-81s=0

a = 18; b = -81; c = 0;
Δ = b2-4ac
Δ = -812-4·18·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-81}{2*18}=\frac{0}{36}
=0
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+81}{2*18}=\frac{162}{36}
=4+1/2
$