2+2s=4/3s+13

Solution for 2+2s=4/3s+13 equation:

2+2s=4/3s+13

We move all terms to the left:

2+2s-(4/3s+13)=0


Domain of the equation: 3s+13)!=0

s∈R


We get rid of parentheses

2s-4/3s-13+2=0

We multiply all the terms by the denominator


2s*3s-13*3s+2*3s-4=0

Wy multiply elements

6s^2-39s+6s-4=0

We add all the numbers together, and all the variables

6s^2-33s-4=0

a = 6; b = -33; c = -4;
Δ = b2-4ac
Δ = -332-4·6·(-4)
Δ = 1185
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{-(-33)-\sqrt{1185}}{2*6}=\frac{33-\sqrt{1185}}{12}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1185}}{2*6}=\frac{33+\sqrt{1185}}{12}
$