2-2s=3/3s+13

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

2-2s=3/3s+13

We move all terms to the left:

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


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

s∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6s^2-39s+6s-3=0

We add all the numbers together, and all the variables

-6s^2-33s-3=0

a = -6; b = -33; c = -3;
Δ = b2-4ac
Δ = -332-4·(-6)·(-3)
Δ = 1017
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{113}}{2*-6}=\frac{33-3\sqrt{113}}{-12}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{113}}{2*-6}=\frac{33+3\sqrt{113}}{-12}
$